a_doob_martingale_combinatorial | axiom | Doob martingale (combinatorial)
a_erdos_renyi_gnm | axiom | Erdos-Renyi G(n,m) model
a_property_b_hypergraph | axiom | Property B of a hypergraph
s_2_kappa_bounded_in_quotient | state | 2 kappa bounded in quotient
s_AD_equiconsistent_woodins | theorem | AD equiconsistent with infinitely many Woodins
s_AD_implies_PSP | theorem | AD implies perfect set property for all sets
s_AD_implies_baire_property | theorem | AD implies the Baire property for all sets
s_AD_implies_measurable | theorem | AD implies all sets Lebesgue measurable
s_AD_in_L_R | theorem | AD in L(ℝ) from large cardinals (Woodin)
s_CZ_lemma_dyadic | theorem | Calderón–Zygmund lemma (dyadic version)
s_GCH_in_L | theorem | V=L implies GCH in L
s_G_acts_on_tree_with_finite_edge_stabilizers | state | G acts on tree with finite edge stabilizers
s_HOD_R_ordinals_inner_model | state | HOD R ordinals inner model
s_H_action_on_bass_serre_tree | state | H action on bass serre tree
s_L1_L_inf_endpoint | state | L1 L inf endpoint
s_L1_bounded_martingale | axiom | L1 bounded martingale
s_L_as_kG_module | state | L as kG module
s_L_hierarchy_L_alpha | state | L hierarchy L alpha
s_L_models_ZF | state | L models ZF
s_L_of_A | state | Constructible closure L(A)
s_Lp_bounded_martingale | axiom | Lp bounded martingale
s_MA_aleph0_theorem | theorem | MA_{ℵ₀} is a theorem of ZFC
s_MA_aleph1_negates_CH | theorem | MA_{ℵ₁} implies ¬CH
s_MA_implies_SH | theorem | Martin's axiom and Suslin's hypothesis
s_MA_measure_category | theorem | MA and additivity of measure/category
s_M_bar_equals_L_beta | state | M bar equals L beta
s_OS_axioms_reflection_positivity | axiom | OS axioms reflection positivity
s_PA_proof_theoretic_ordinal_epsilon_0 | theorem | Specker–Ackermann ordinal of PA / Gentzen analysis
s_PFA_consequences | theorem | Proper Forcing Axiom consequences (Todorčević)
s_TV_distance_to_stationary_renewal_zero | state | TV distance to stationary renewal zero
s_T_as_ccc_poset | state | T as ccc poset
s_a_e_convergent_bounded_L_p_sequence | axiom | a e convergent bounded L p sequence
s_a_s_convergence_via_levy_equivalence | state | a s convergence via levy equivalence
s_abelian_l_equals_hecke | theorem | Abelian Artin L-function equals Hecke L-function
s_abscissa_of_absolute_convergence | axiom | Abscissa of absolute convergence
s_abscissa_relation | theorem | Abscissa of convergence vs absolute convergence relation
s_absolute_coequalizer | axiom | Absolute coequalizer
s_absolute_convergence | state | Absolute convergence
s_absolute_convergence_fourier_smoothness | theorem | Absolute convergence of Fourier series under smoothness
s_absolute_convergence_implies_convergence | theorem | Absolute convergence implies convergence
s_absolute_convergence_of_improper_integrals | theorem | Absolute convergence of improper integrals
s_absolute_galois_group | state | Absolute Galois group Gal(K^sep/K)
s_absolute_value_on_R | state | Absolute value (on R)
s_absolute_value_on_a_field | axiom | Absolute value on a field
s_absolute_value_product_formula | axiom | absolute_value_product_formula
s_absolutely_continuous_function | axiom | Absolutely continuous function
s_absolutely_continuous_function_g | axiom | absolutely continuous function g
s_absolutely_continuous_measure | axiom | Absolutely continuous measure
s_absolutely_normal_number | axiom | Absolutely normal number
s_absoluteness_to_L | state | absoluteness to L
s_absorption_infinite_cardinals | theorem | Absorption law for infinite cardinals
s_ac_function_measure_correspondence | theorem | AC functions and absolute continuity of measures
s_ac_maps_null_to_null | theorem | Absolutely continuous functions map null sets to null sets
s_adian_rabin_theorem | theorem | Adian–Rabin theorem on Markov properties
s_adjoint_operator_L_star | state | adjoint operator L star
s_aep | theorem | Asymptotic Equipartition Property (AEP)
s_aleph_function | state | Aleph function ℵ_α
s_aleph_numbers | state | aleph numbers ℵ_α
s_alladi_erdos_largest_prime_factor_average | theorem | Alladi–Erdős result on average of log P⁺(n)
s_amenable_property_T_clash | state | amenable property T clash
s_analytic_baire_property | theorem | Analytic sets have the Baire property
s_analytic_continuation_L_function_s_gt_0 | theorem | Analytic continuation of L(s,χ) to Re(s) > 0
s_analytic_continuation_l_all_c | theorem | Analytic continuation of L(s,χ) to all of ℂ
s_analytic_continuation_l_re_gt_0 | theorem | Analytic continuation of L(s,χ) to Re(s) > 0
s_analytic_determinacy | theorem | Analytic determinacy
s_analytic_measurable | theorem | Analytic sets are Lebesgue measurable
s_analytic_psp | theorem | Analytic sets have the perfect set property
s_antichain_in_boolean_lattice | axiom | antichain in boolean lattice
s_aps_in_pseudorandom_dense_subset | state | APs in pseudorandom dense subset
s_archimedean_property | theorem | Archimedean property
s_aronszajn_tree | state | Aronszajn tree
s_aronszajn_tree_existence | theorem | Existence of an Aronszajn tree
s_artin_l_function | axiom | artin l function
s_artinian_ring_finitely_many_maximal_ideals | theorem | Artinian ring has finitely many maximal ideals
s_artins_lemma_on_fixed_fields | theorem | Artin's lemma on fixed fields
s_asymptotic_expansion_of_the_gamma_function | state | Asymptotic expansion of the gamma function
s_atomic_partition_construction | state | atomic partition construction
s_attached_primes | axiom | Attached primes
s_attained_extrema_on_closed_interval | state | attained extrema on closed interval
s_augmentation_ideal | axiom | Augmentation ideal I_G
s_average_order_of_sigma_n | theorem | Average order of σ(n)
s_axiom_of_choice | axiom | Axiom of choice
s_axiom_of_choice_function_phi | state | axiom of choice function phi
s_axiom_of_determinacy_for_borel_games | axiom | axiom of determinacy for borel games
s_azuma_hoeffding | theorem | Azuma–Hoeffding Inequality
s_backward_martingale | axiom | Backward (reversed) martingale
s_backward_martingale_convergence | theorem | Backward martingale convergence theorem
s_baire_sigma_algebra | axiom | Baire σ-algebra
s_bakergillsolovay_relativization_barrier | theorem | Baker-Gill-Solovay relativization barrier
s_basic_properties_fourier_transform | theorem | Basic properties of the Fourier transform on ℝ
s_basic_set_partition | state | basic set partition
s_bass_serre_tree_for_free_product | state | bass serre tree for free product
s_beatty_partition_count_match | state | beatty partition count match
s_behrend_3_ap_free_set | theorem | Behrend's construction of dense 3-AP-free set
s_bernstein_theorem_monotonic | theorem | Bernstein's theorem on absolutely monotonic functions
s_beth_definability | theorem | Beth's definability theorem
s_beth_function | state | Beth function ℶ_α
s_bethe_ansatz_xxx_theorem | theorem | Bethe ansatz solution of the Heisenberg XXX chain
s_bethe_equations | state | bethe equations
s_block_cut_tree | state | Block-cut tree
s_bm_as_martingale | state | Brownian motion as a martingale
s_bm_path_properties | state | Path properties of Brownian motion
s_bm_scaling_property | theorem | Scaling property of Brownian motion
s_bochner_martinelli_kernel | state | Bochner–Martinelli kernel
s_boolean_algebra_B | state | boolean algebra B
s_boolean_circuit | axiom | Boolean circuit
s_boolean_function_def | axiom | Boolean function
s_boolean_lattice | axiom | Boolean lattice B_n
s_boolean_prime_ideal_theorem | theorem | Boolean Prime Ideal Theorem
s_boolean_satisfiability | state | boolean_satisfiability
s_boolean_valued_models | state | boolean_valued_models
s_boolean_valued_universe | state | Boolean-valued universe V^B
s_booleanvalued_model | state | Boolean-valued model
s_borel_measurable_function | state | Borel measurable function
s_borel_sigma_algebra_on_R | axiom | borel sigma algebra on R
s_borel_sigma_algebra_on_Rn | axiom | Borel σ-algebra on ℝⁿ
s_bott_iteration_formula | theorem | Bott's iteration formula
s_bounded_differences_for_martingale | state | bounded differences for martingale
s_bowen_partition_function_Z_n | state | bowen partition function Z n
s_bowen_specification_unique_equilibrium | theorem | Bowen's specification property implies unique equilibrium
s_bubble_tree_at_singular_points | state | bubble tree at singular points
s_cameron_martin_space_H1 | axiom | cameron martin space H1
s_cameron_martin_theorem | theorem | Cameron–Martin Theorem
s_candidate_closure_properties | state | candidate closure properties
s_candidate_generating_partition | state | candidate generating partition
s_canfield_erdos_pomerance_theorem | theorem | Canfield–Erdős–Pomerance theorem
s_canonical_ramsey_theorem | theorem | Canonical Ramsey theorem (Erdős–Rado)
s_canonical_reflection | state | canonical reflection
s_caratheodory_measurability | axiom | Carathéodory measurability (μ*-measurable set)
s_cardinal_arithmetic | state | Cardinal arithmetic
s_cardinal_number | axiom | Cardinal number
s_cartesian_closed_category | axiom | Cartesian closed category
s_cauchy_filter | axiom | Cauchy filter
s_cauchy_lemma_polygonal | theorem | Cauchy’s lemma (polygonal numbers)
s_cayley_tree_of_F | state | cayley tree of F
s_cc_dense_in_lp | theorem | Density of Cc in Lp for Radon measures
s_ccc_forcing | state | Countable chain condition (ccc)
s_ccc_partial_order | axiom | ccc partial order
s_ccc_preserves_cardinals | theorem | ccc forcing preserves cardinals
s_centered_random_walk_martingale | state | centered random walk martingale
s_central_force_problem | axiom | central force problem
s_cesaro_average_iterates_in_K | state | cesaro average iterates in K
s_cf_parse_tree_pumping_step | state | cf parse tree pumping step
s_cft_modular_invariance_theorem | theorem | Modular invariance of CFT partition function (S, T action)
s_ch_independent_of_zfc | theorem | CH independent of ZFC
s_chain_meets_antichain_at_most_once | state | chain meets antichain at most once
s_character_of_verma_module | state | Character of a Verma module
s_chevalley_constructibility | theorem | Chevalley constructibility theorem
s_chevalley_theorem_constructible_sets | theorem | Chevalley's theorem on constructible sets
s_chvatal_erdos_target | state | chvatal erdos target
s_chvatal_erdos_theorem | theorem | Chvátal–Erdős theorem
s_chvatal_erdos_theorem_diestel | theorem | Chvátal–Erdős theorem
s_circle_orbit_partition | state | circle orbit partition
s_class_D_submartingale | axiom | class D submartingale
s_classifying_space_B_sigma_infty | state | classifying space B sigma infty
s_cleaned_reduced_graph_H_free_or_dense | state | cleaned reduced graph H free or dense
s_closed_forcing_adds_no_sequences | theorem | <κ-closed forcing adds no new <κ-sequences
s_closed_ideal_in_Wiener_algebra | state | closed ideal in Wiener algebra
s_closure_measurable_functions_under_limits | theorem | Closure of measurable functions under limits
s_club_filter | state | Club filter
s_club_intersection_theorem | theorem | Intersection of clubs is club
s_club_principle | state | Club principle ♣
s_club_set | state | Closed unbounded (club) set
s_cluster_point_of_filter | state | Cluster point of a filter
s_cm_equidimensional | theorem | Cohen-Macaulay local rings are equidimensional
s_cm_implies_catenary | theorem | Cohen-Macaulay rings are universally catenary
s_cm_polynomial_ring | theorem | Polynomial rings over Cohen-Macaulay rings are Cohen-Macaulay
s_codimension_of_an_ideal | state | Codimension (height) of an ideal
s_cofinality | state | Cofinality cf(α)
s_coheight_of_a_prime_ideal | axiom | Coheight of a prime ideal
s_cohen_forcing | theorem | Cohen's forcing theorems
s_cohen_forcing_is_ccc | theorem | Cohen forcing is ccc
s_cohen_independence_of_ch | theorem | cohen_independence_of_ch
s_cohen_macaulay_ring | axiom | Cohen–Macaulay ring
s_cohen_structure_theorem | theorem | Cohen structure theorem
s_cohen_structure_theorem_mixed_char | theorem | Cohen structure theorem (mixed characteristic)
s_cohenmacaulay_module | axiom | Cohen-Macaulay module
s_cohens_independence_of_ch | theorem | Cohen's independence of CH
s_collapse_function_pi | state | collapse function pi
s_collapse_map_to_thom_space | state | collapse map to thom space
s_collapse_to_MO_k_thom_space | state | collapse to MO k thom space
s_collapsed_substructure_is_L_alpha | state | collapsed substructure is L alpha
s_comma_categories_contractible | axiom | comma categories contractible
s_comma_category | axiom | Comma category
s_compact_3_manifold_with_simply_connected_sphere_property | axiom | compact 3 manifold with simply connected sphere property
s_compact_hyperbolic_surface_Gamma_minus_H2 | axiom | compact hyperbolic surface Gamma minus H2
s_compact_operators_closed_ideal | theorem | Compact operators form a closed ideal
s_compact_smooth_moduli_under_generic_metric | state | compact smooth moduli under generic metric
s_compactness_principle_ramsey | theorem | Compactness principle for Ramsey theory
s_compatible_conditions | state | Compatible and incompatible conditions
s_compensated_martingale | state | compensated martingale
s_complete_BA_for_random_forcing | state | complete BA for random forcing
s_complete_boolean_algebra | axiom | Complete Boolean algebra
s_completed_l_function | axiom | Completed L-function
s_completeness_of_R | axiom | Completeness of R (least upper bound property)
s_complexity_class_l_logspace | state | complexity class L (logspace)
s_con_MA_not_CH | theorem | Con(MA+¬CH) (Solovay–Tennenbaum)
s_con_SH | theorem | Con(SH) (Solovay–Tennenbaum)
s_con_zfc_gch | theorem | Con(ZFC) ⇒ Con(ZFC+GCH) (Gödel)
s_con_zfc_not_ch_cohen | theorem | Con(ZFC)⟹Con(ZFC+¬CH) (Cohen)
s_conductor_ideal | state | Conductor ideal
s_conductor_l_function | axiom | Conductor of an L-function
s_congruence_subgroup_gamma0 | axiom | Congruence subgroup Γ₀(N)
s_congruence_subgroup_gamma1 | axiom | Congruence subgroup Γ₁(N)
s_conjugate_partition | state | Conjugate (transpose) partition
s_construct_tree_killing_each_predicted_antichain | state | construct tree killing each predicted antichain
s_constructible_closure_L_R | axiom | constructible closure L R
s_constructible_reals | state | Constructible reals ℝ∩L
s_constructible_universe_L | theorem | Constructible universe L (Gödel)
s_constructible_wellordering | state | Constructible well-ordering <_L
s_continuity_via_filters | theorem | Continuity via filters
s_continuous_functions_are_measurable | theorem | Continuous functions are Borel measurable
s_continuous_local_martingale_M_t | axiom | continuous local martingale M t
s_continuous_spectrum_gamma_h | axiom | Continuous spectrum of Γ\H
s_continuum_hypothesis_or_GCH | axiom | continuum hypothesis or GCH
s_contraction_property_of_resolvent | state | contraction property of resolvent
s_convergence_l_nonprincipal_s_gt_0 | theorem | Convergence of L(s,χ) for nonprincipal χ at s > 0
s_convergence_of_filter | axiom | Convergence of a filter
s_convergent_quadratic_iteration | state | convergent quadratic iteration
s_converse_mean_value_property | theorem | Converse of the mean value property
s_convexity_bound_l_functions | theorem | Convexity bound for L-functions
s_coprime_ideals | axiom | Coprime ideals
s_cops_and_robber | state | Cops and robbers characterization of tree-width
s_correspondence_between_forms_and_ideals | theorem | Correspondence between forms and ideals
s_coset_partition_of_G | state | coset partition of G
s_coulomb_phase_shift | state | Coulomb Phase Shift sigma_l(eta)
s_countable_closed_partition_hypothesis | state | countable closed partition hypothesis
s_countable_dense_sequence_in_unit_ball | state | countable dense sequence in unit ball
s_countable_dense_subset_of_X | state | countable dense subset of X
s_countable_markov_partition | state | countable markov partition
s_countable_proper_forcing_class | axiom | countable proper forcing class
s_counting_ideals_of_bounded_norm | theorem | Counting ideals of bounded norm
s_counting_lemma_dense_H_implication | state | counting lemma dense H implication
s_curve_l_function_eigenvalues | state | curve l function eigenvalues
s_curve_recovered_from_kappa_tau | state | curve recovered from kappa tau
s_cycle_lemma_count | state | cycle lemma count
s_davenport_erdos_density_multiples | theorem | Davenport–Erdős theorem on multiples
s_decay_of_dual_iterates | state | decay of dual iterates
s_decision_tree_complexity | axiom | Decision tree complexity
s_definability_in_L_alpha | axiom | definability in L alpha
s_definability_lemma_forcing | theorem | Definability lemma (forcing)
s_defocusing_property_on_arcs | state | defocusing property on arcs
s_degeneration_at_E2 | state | Degeneration at E_2
s_degree_l_function | axiom | Degree of an L-function
s_deletion_property | theorem | Deletion property
s_dense_domain_with_skew_adjoint_generator | state | dense domain with skew adjoint generator
s_dense_family_of_analytic_test_functions | state | dense family of analytic test functions
s_dense_functor | axiom | Dense functor
s_dense_predense | state | Dense and predense sets
s_dense_ring_of_linear_transformations | state | Dense ring of linear transformations
s_dense_set | axiom | Dense set
s_dense_set_of_explicit_stochastic_integrals | state | dense set of explicit stochastic integrals
s_dense_subspaces_of_lp | theorem | Dense subspaces of Lp
s_densely_defined_closed_linear_operator | axiom | densely defined closed linear operator
s_densely_defined_closed_operator_A | axiom | densely defined closed operator A
s_densely_defined_closed_operator_T | axiom | densely defined closed operator T
s_densely_defined_dissipative_operator_A | axiom | densely defined dissipative operator A
s_density_increment_iteration | state | density increment iteration
s_density_of_zeros_near_sigma_1 | state | Density of zeros near σ = 1
s_derandomized_ramsey_bound | theorem | Derandomized Ramsey lower bound
s_descent_on_ideal_chain | state | descent on ideal chain
s_determinacy_ad | state | determinacy (AD)
s_determinacy_of_a_set | state | Determinacy of a set Det(A)
s_determinantal_ideal | axiom | Determinantal ideal
s_diagonal_intersection_club | state | diagonal intersection club
s_diagonal_ramsey_bounds | state | Diagonal Ramsey number bounds
s_diamond_anticipates_antichains | state | diamond anticipates antichains
s_diamond_holds_in_L | theorem | ◊ holds in L (Jensen)
s_diamond_implies_ch | theorem | ◊ implies CH
s_diamond_implies_suslin_tree | theorem | Suslin's hypothesis / ◊ implies a Suslin tree (Jensen)
s_diamond_iso_map | state | diamond iso map
s_diamond_principle_on_omega_1 | axiom | diamond principle on omega 1
s_different_ideal_definition | state | different ideal definition
s_diffusion_generator_L_with_carre_du_champ | axiom | diffusion generator L with carre du champ
s_digamma_function | state | Digamma function
s_dilation_property_lebesgue | theorem | Dilation property of Lebesgue measure
s_dimension_reduction_via_suslin | state | dimension reduction via suslin
s_dimension_via_m_primary_ideals | theorem | Dimension via 𝔪-primary ideals
s_direct_limit_filtered_colimit | axiom | Direct limit (filtered colimit)
s_dirichlet_l_function | axiom | dirichlet l function
s_dirichlet_l_nonvanishing_at_1 | theorem | dirichlet_l_nonvanishing_at_1
s_discrete_spectrum_gamma_h | axiom | Discrete spectrum of Γ\H
s_dispersive_L_infty_to_L_1_estimate | state | dispersive L infty to L 1 estimate
s_distance_decreasing_property | state | distance decreasing property
s_distance_to_dense_coords | state | distance to dense coords
s_divergence_form_elliptic_with_L_infty_coefficients | axiom | divergence form elliptic with L infty coefficients
s_divergence_form_parabolic_with_L_infty_coeff | axiom | divergence form parabolic with L infty coeff
s_divisor_function_sigma_alpha | axiom | Generalized divisor function σ_α
s_doob_Lp_convergence | theorem | Doob L^p Martingale Convergence
s_doob_filtration_martingale | state | doob filtration martingale
s_doob_martingale_convergence | theorem | Doob's martingale convergence theorem
s_doob_martingale_convergence_as | theorem | Doob's Martingale Convergence (a.s.)
s_duality_maximal_cm_modules | theorem | Duality for maximal Cohen-Macaulay modules
s_dynkin_martingale | state | dynkin martingale
s_each_fibre_nonstationary | state | each fibre nonstationary
s_easton_admissible_F | state | easton admissible F
s_easton_class_forcing | state | easton class forcing
s_easton_theorem | theorem | Easton's theorem on continuum function
s_edge_coloring | axiom | Proper edge coloring
s_eigenmeasure_for_L_phi | state | eigenmeasure for L phi
s_elementary_embedding_j_V_to_V | axiom | elementary embedding j V to V
s_elementary_substructure_of_L_alpha | state | elementary substructure of L alpha
s_elementary_substructure_property | axiom | elementary substructure property
s_elimination_ideal | state | elimination ideal
s_ellipsoid_volume_shrinkage_iteration | state | ellipsoid volume shrinkage iteration
s_elliptic_operator_L_constant_coeff | axiom | elliptic operator L constant coeff
s_elliptic_operator_L_self_adjoint | axiom | elliptic operator L self adjoint
s_elliptic_operator_L_with_C_alpha_coefficients | axiom | elliptic operator L with C alpha coefficients
s_empirical_measure_L_n | axiom | empirical measure L n
s_equilibrium_renewal_distribution | state | Equilibrium (stationary) renewal distribution
s_equivalence_class_partition_theorem | theorem | Equivalence class partition theorem
s_equivalence_of_absolute_values | axiom | equivalence of absolute values
s_equivalence_of_nets_and_filters | theorem | Equivalence of nets and filters
s_erdos_cardinal | state | Erdős cardinal κ→(α)^{<ω}
s_erdos_essential_components_theorem | theorem | Erdős’s theorem on essential components
s_erdos_fuchs_theorem | theorem | Erdős–Fuchs theorem
s_erdos_gallai_theorem | theorem | Erdős–Gallai theorem (graphic sequence)
s_erdos_ginzburg_ziv_theorem | theorem | Erdős–Ginzburg–Ziv theorem
s_erdos_girth_chromatic | theorem | Erdős theorem on girth and chromatic number
s_erdos_heilbronn_conjecture | theorem | Erdős–Heilbronn conjecture (Dias da Silva–Hamidoune)
s_erdos_implies_zero_sharp | theorem | κ→(ω₁)^{<ω} implies 0# exists
s_erdos_kac_theorem | theorem | Erdős–Kac theorem
s_erdos_ko_rado | theorem | Erdős–Ko–Rado theorem
s_erdos_ko_rado_theorem | theorem | Erdős–Ko–Rado theorem
s_erdos_littlewood_offord | theorem | Erdős–Littlewood–Offord inequality
s_erdos_posa_dual_target | state | erdos posa dual target
s_erdos_posa_theorem | theorem | Erdős–Pósa theorem
s_erdos_rado_theorem | theorem | Erdős–Rado theorem
s_erdos_ramsey_lower | theorem | Erdős probabilistic lower bound for Ramsey numbers
s_erdos_ramsey_lower_bound | theorem | Erdős probabilistic lower bound on R(k,k)
s_erdos_renyi_connectedness_threshold | theorem | Erdős–Rényi Connectedness Threshold
s_erdos_renyi_connectivity_threshold | theorem | Erdős–Rényi threshold for connectivity
s_erdos_renyi_giant_component | theorem | Erdős–Rényi Giant Component Threshold
s_erdos_renyi_graph_G_n_p | axiom | erdos renyi graph G n p
s_erdos_renyi_model | axiom | Erdős–Rényi random graph model G(n, p)
s_erdos_stone_target | state | erdos stone target
s_erdos_stone_theorem | theorem | Erdős–Stone theorem
s_erdos_szekeres_ramsey_bound | theorem | Erdős–Szekeres bound on Ramsey numbers
s_erdos_szekeres_theorem | theorem | Erdős–Szekeres monotone subsequence theorem
s_erdos_szemeredi_conjecture | state | Erdős–Szemerédi sum-product conjecture
s_erdos_szemeredi_sum_product | theorem | Erdős–Szemerédi sum–product
s_erdos_tarski_theorem | theorem | Erdős–Tarski theorem on weakly compact cardinals
s_erdos_turan_inequality | theorem | Erdős-Turán inequality
s_erdos_wintner_theorem | theorem | Erdős–Wintner theorem
s_erdos_woods_conjecture_consequence | theorem | erdos_woods_conjecture_consequence
s_euler_four_square_identity | axiom | Euler four-square identity
s_euler_partition_identity | theorem | Euler's partition identity
s_euler_product_for_l_function | theorem | Euler product for L(s,χ)
s_euler_reflection_formula | theorem | Euler's Reflection Formula
s_eventuality_filter | state | Eventuality filter (filter generated by a net)
s_every_ideal_is_finite_intersection_of_irreducibles | theorem | Every ideal is a finite intersection of irreducible ideals
s_every_maximal_ideal_is_prime | theorem | Every maximal ideal is prime
s_every_measurable_limit_of_simple | theorem | Every measurable function is a limit of simple functions
s_evolution_equation_with_lax_pair_L_M | axiom | evolution equation with lax pair L M
s_exchange_property | theorem | Exchange property
s_exchangeable_sigma_algebra | axiom | exchangeable sigma algebra
s_existence_of_ultrafilters | theorem | Existence of ultrafilters (ultrafilter lemma)
s_existence_uniqueness_stationary | theorem | Existence and uniqueness of stationary distribution
s_exp_lambda_M_n_is_supermartingale | state | exp lambda M n is supermartingale
s_expected_codimension_determinantal | theorem | Expected codimension of determinantal ideals
s_exponential_local_martingale_e_ixiM | state | exponential local martingale e ixiM
s_exponential_martingale | state | Exponential martingale
s_extension_and_contraction_of_ideals | axiom | Extension and contraction of ideals
s_extension_of_absolute_values | theorem | Extension of absolute values
s_f_sigma_set | axiom | F_σ set
s_faddeev_popov_partition_function_theorem | theorem | Faddeev–Popov gauge-fixing procedure
s_family_indexed_by_dense_subset_D | state | family indexed by dense subset D
s_farey_mediant_theorem | theorem | Farey mediant property
s_farey_neighbor_theorem | theorem | Farey neighbor property
s_feller_property_markov_chain | axiom | Feller property (Markov chain on topological space)
s_fermat_right_triangle_no_rational_square_area | theorem | Fermat's right-triangle theorem
s_fermat_two_square_theorem | theorem | Fermat's two-square theorem
s_ferromagnetic_ising_partition_function | axiom | ferromagnetic ising partition function
s_field_extension_L_over_K | axiom | Field extension L/K
s_filter | axiom | Filter
s_filter_base | axiom | Filter base (basis of a filter)
s_filter_characterization_compactness | theorem | Filter characterization of compactness
s_filter_generated_by_base | state | Filter generated by a base
s_filtered_category | axiom | Filtered category
s_filtered_colimit_algebraic | theorem | Filtered colimits in algebraic categories
s_filtered_colimits_commute_finite_limits | theorem | Filtered colimits commute with finite limits in Set
s_filtered_complex | axiom | Filtered complex
s_filtered_module | axiom | Filtered module
s_filtered_probability_space | axiom | filtered probability space
s_filtered_ring | axiom | Filtered ring
s_final_functor | axiom | Final functor (cofinal)
s_finitary_TREE_function_statement | state | finitary TREE function statement
s_finite_generating_set_of_ideal | state | Finite generating set of ideal
s_finite_intersection_property | theorem | Finite intersection property characterization of compactness
s_finite_labelled_trees | axiom | finite labelled trees
s_finite_normal_separable_extension_L_over_K | state | Finite normal separable extension L/K
s_finite_product_of_finitely_branching_trees | axiom | finite product of finitely branching trees
s_finite_proper_time_to_focal_point | state | finite proper time to focal point
s_finite_ramsey_conjecture | state | finite ramsey conjecture
s_finite_rooted_tree | axiom | finite rooted tree
s_finite_signed_measure_nu_absolutely_continuous | state | finite signed measure nu absolutely continuous
s_finite_witness_property | state | finite witness property
s_first_order_graph_property_phi | axiom | first order graph property phi
s_fitting_ideal | state | Fitting ideal
s_fitting_ideals_and_annihilator | theorem | Fitting ideals and annihilator
s_flat_degeneration_to_initial_ideal | theorem | Flat degeneration to initial ideal
s_flatness_ideal_criterion | theorem | Ideal-theoretic characterization of flatness
s_flatness_is_a_local_property | theorem | Flatness is a local property
s_floating_lp_iteration | state | floating lp iteration
s_fodor_constancy_on_stationary_subset | state | fodor constancy on stationary subset
s_fodor_lemma | theorem | Fodor's pressing-down lemma
s_forcing | state | forcing
s_forcing_extension_mg | state | forcing extension M[G]
s_forcing_relation | state | Forcing relation p⊩φ
s_forcing_theorem | theorem | Forcing theorem (fundamental)
s_formal_adjoint_operator_L_star | state | formal adjoint operator L star
s_fractional_ideal | axiom | fractional_ideal
s_fractional_ideals_of_dedekind_domains_are_invertible | theorem | Fractional ideals of Dedekind domains are invertible
s_fredholm_property_elliptic_bvp | theorem | Fredholm property for elliptic BVPs
s_fredholm_property_elliptic_compact_manifold | theorem | Fredholm property of elliptic operators on compact manifolds
s_fs_iteration_ccc | theorem | FS iteration of ccc is ccc
s_full_modularity_theorem_BCDT | theorem | Modularity Theorem — full, Breuil–Conrad–Diamond–Taylor 2001
s_function_with_absolutely_convergent_fourier_series_nonvanishing | axiom | function with absolutely convergent fourier series nonvanishing
s_functional_equation_l_primitive | theorem | Functional equation of L(s,χ) for primitive characters
s_fundamental_lemma_ngo | theorem | Fundamental lemma (Ngô)
s_fundamental_lemma_of_sieve | theorem | Brun–Hooley sieve / linear sieve fundamental lemma
s_fundamental_theorem_of_p_partitions | theorem | Fundamental theorem of P-partitions (Stanley)
s_gale_stewart_theorem | theorem | Gale–Stewart theorem
s_galois_extension_L_over_K | axiom | galois extension L over K
s_galois_extension_l_over_k | axiom | galois extension l over k
s_galvin_prikry_game | state | galvin prikry game
s_galvin_prikry_theorem | theorem | Galvin–Prikry theorem
s_gamma_2_operator | state | gamma 2 operator
s_gamma_analytic_continuation | theorem | Analytic continuation of Γ to meromorphic function on ℂ
s_gamma_analyticity | theorem | Gamma function is analytic on the right half-plane
s_gamma_convergence | state | Γ-convergence
s_gamma_distribution | axiom | Gamma distribution
s_gamma_factors_functional_equation | axiom | Gamma factors in functional equations
s_gamma_function | state | Gamma function
s_gamma_recurrence | theorem | Gamma function recurrence relation
s_gamma_recurrence_relation | theorem | Gamma Function Recurrence Relation
s_gauss_constructible_regular_polygons | theorem | Gauss's theorem on constructible regular polygons
s_gauss_lemma_legendre | theorem | Gauss's lemma for the Legendre symbol
s_gauss_lemma_polynomials | theorem | Gauss's lemma (polynomials)
s_gauss_lemma_riemannian | theorem | Gauss lemma (Riemannian geometry)
s_gausss_lemma_content_of_polynomials | theorem | Gauss's lemma (content of polynomials)
s_gausss_lemma_quadratic_residues | theorem | Gauss's lemma (quadratic residues)
s_gelfand_spectrum | state | Gelfand spectrum (maximal ideal space)
s_general_l_function_ik | axiom | General L-function (Iwaniec–Kowalski framework)
s_generalized_continuum_hypothesis | state | Generalized Continuum Hypothesis (GCH)
s_generic_H_meets_X_transversely | state | generic H meets X transversely
s_generic_extension_V_G | state | generic extension V G
s_generic_extension_with_F | state | generic extension with F
s_generic_filter | state | generic filter
s_generic_filter_2 | state | generic_filter
s_generic_flatness_theorem | theorem | Generic flatness theorem
s_generic_freeness_lemma | theorem | Generic freeness lemma (Grothendieck)
s_generic_parameter_makes_f_transverse | state | generic parameter makes f transverse
s_generic_point_of_a_scheme | state | generic point of a scheme
s_generic_projection_remains_immersion | state | generic projection remains immersion
s_generic_random_real | state | generic random real
s_generic_section_connected | state | generic section connected
s_generic_smoothness | theorem | Generic smoothness
s_generic_specialization_remains_irreducible | state | generic specialization remains irreducible
s_generic_ultrapower | state | generic ultrapower
s_gessels_formula_p_partitions | theorem | Gessel's formula for P-partitions
s_gimel_function | state | Gimel function ℷ(κ)
s_glued_proper_overscheme_X_bar | state | glued proper overscheme X bar
s_godel_L_model | state | Gödel L model (alias)
s_goedel_constructibility | theorem | goedel_constructibility
s_going_up_theorem | theorem | Going-up theorem (Cohen–Seidenberg)
s_grade_of_an_ideal | state | Grade of an ideal
s_graph_property_testability | theorem | Testability of hereditary graph properties
s_graph_ramsey_number | axiom | Graph Ramsey number R(G, H)
s_graph_ramsey_theory | state | graph Ramsey theory
s_graph_removal_lemma_diestel | theorem | Graph removal lemma
s_group_type_fp | axiom | Group of type FP
s_growth_rate_stationary_market | theorem | Asymptotic optimality of log-optimal investment (AEP for investment)
s_hardy_ramanujan_partition_asymptotic | theorem | Hardy–Ramanujan partition asymptotic
s_harmonic_mvp_characterization | theorem | Mean value property characterizes harmonic functions
s_hawking_temperature_kappa_over_2pi | state | hawking temperature kappa over 2pi
s_hecke_l_function_grossencharakter | axiom | Hecke L-function
s_height_of_a_prime_ideal | axiom | Height of a prime ideal
s_hensels_lemma_2 | theorem | hensels_lemma
s_hereditarily_small_sets_H_kappa | state | Hereditarily small sets H(κ)
s_hessenberg_kappa_squared | theorem | Hessenberg's theorem (κ²=κ)
s_hilbert_symbol_properties | theorem | Bilinearity and non-degeneracy of the Hilbert symbol
s_hochster_big_cm_modules | theorem | Hochster's theorem on big Cohen-Macaulay modules
s_hodge_diamond | state | Hodge diamond
s_homogeneous_ideal | axiom | homogeneous ideal
s_homogeneous_tree_for_T | state | homogeneous tree for T
s_homotopy_extension_property | axiom | Homotopy extension property
s_homotopy_grid_partition | state | homotopy grid partition
s_homotopy_lifting_property | theorem | Homotopy lifting property
s_hrushovski_generic_structure | state | hrushovski generic structure
s_huge_cardinal | state | Huge cardinal
s_hydra_ordinal_invariant | state | hydra ordinal invariant
s_hypergraph_ramsey_number | state | Hypergraph Ramsey number
s_hypothetical_suslin_tree | state | hypothetical suslin tree
s_ideal_I | state | Ideal I
s_ideal_a_b_in_R | state | ideal a b in R
s_ideal_as_maximal_minors | state | ideal as maximal minors
s_ideal_class_group | state | Ideal class group
s_ideal_class_group_2 | axiom | ideal_class_group
s_ideal_in_R_x | state | Ideal in R[x]
s_ideal_lattice | state | Ideal lattice
s_ideal_of_a_ring | axiom | Ideal (of a ring)
s_ideal_of_an_algebraic_set | state | ideal of an algebraic set
s_ideal_of_lie_algebra | axiom | Ideal of a Lie algebra
s_ideal_principal_d | state | ideal principal d
s_ideal_product | axiom | Product of ideals
s_ideal_quotient | axiom | Ideal quotient (colon ideal)
s_ideal_set_theory | axiom | Ideal (set-theoretic)
s_ideal_sheaf | state | Ideal sheaf
s_ideal_sum | axiom | Sum of ideals
s_ideal_theory_group_algebra | state | Ideal theory of L¹(G)
s_ideal_waring_conjecture | state | Ideal Waring conjecture
s_ideal_with_n_generators | axiom | ideal with n generators
s_ideals_quotient_banach_algebra | axiom | Ideals and quotient algebras in Banach algebras
s_improper_integral | axiom | Improper integral (convergent integral on unbounded interval)
s_inaccessible_cardinal_axiom | axiom | inaccessible cardinal axiom
s_incidence_matrix_factorisation_L_eq_B_B_T | state | incidence matrix factorisation L eq B B T
s_independence_of_sigma_algebras | axiom | Independence of σ-algebras
s_index_equals_L_genus_pairing | state | index equals L genus pairing
s_index_homomorphism | theorem | Homomorphism properties of the index function
s_indiscernibility_of_uncountable_cardinals | state | indiscernibility of uncountable cardinals
s_induced_character_l_series_factorization | theorem | Induced character and L-series factorization
s_infinitely_many_woodin_cardinals | axiom | infinitely many woodin cardinals
s_initial_ideal | state | Initial ideal
s_initial_ordinal | state | Initial ordinal
s_integer_partitions | axiom | integer partitions
s_integral_nonneg_measurable_function | axiom | Integral of a nonnegative measurable function
s_integration_by_parts_ac | theorem | Integration by parts for absolutely continuous functions
s_intermediate_value_nonatomic | theorem | Intermediate value property for non-atomic measures
s_intersecting_family_property | axiom | intersecting family property
s_invariant_partition_C_D | state | invariant partition C D
s_invariant_sigma_algebra | state | Invariant σ-algebra of a measure-preserving transformation
s_invertible_ideal | state | Invertible ideal
s_irreducible_ideal | axiom | Irreducible ideal
s_irreducible_ideals_are_primary_in_noetherian_rings | theorem | Irreducible ideals are primary in Noetherian rings
s_isolated_types_dense_iff_omega_categorical | state | isolated types dense iff omega categorical
s_isolation_lemma_mvv | theorem | Isolation lemma (Mulmuley–Vazirani–Vazirani)
s_isolation_lemma_witness | state | isolation lemma witness
s_iterated_critical_points | state | iterated critical points
s_iterated_function_system | axiom | Iterated function system (IFS) as Markov chain
s_iterated_generating_functions_branching | theorem | Iterated generating functions for branching processes
s_iterated_hj_combinatorial_subspace | state | iterated hj combinatorial subspace
s_iterated_holder_on_indicator | state | iterated holder on indicator
s_iterated_neighborhood_of_homoclinic | state | iterated neighborhood of homoclinic
s_iterated_root_adjunction | state | iterated root adjunction
s_iterated_sumset | axiom | Iterated sumset kA
s_iteration_trees_on_V | state | iteration trees on V
s_iterative_orthogonal_eigenbasis | state | iterative orthogonal eigenbasis
s_ito_representation_theorem | theorem | Itô Representation Theorem (martingale representation)
s_jack_polynomial | state | Jack Polynomial P_kappa^{(alpha)}
s_jacobi_four_square_formula | theorem | Jacobi's four-square theorem
s_kappa_categoricity | axiom | kappa categoricity
s_kappa_cc_knaster | state | κ-cc / κ-Knaster
s_kappa_cc_preserves_cardinals | theorem | κ-cc forcing preserves cardinals ≥κ
s_kappa_closed_forcing | state | <κ-closed forcing
s_kappa_complete_filter | axiom | κ-complete filter
s_kappa_prime_sign_change_contradiction | state | kappa prime sign change contradiction
s_kato_smoothness_absolute_continuity | theorem | Kato smoothness implies absolute continuity
s_keisler_shelah_theorem | theorem | Keisler–Shelah ultrapower characterization of elementary equivalence
s_kirchhoff_matrix_tree | theorem | Kirchhoff's matrix tree theorem
s_konig_cardinal_theorem | theorem | König's theorem (cardinal)
s_kostant_partition_function | state | Kostant partition function
s_krull_hauptidealsatz | theorem | Krull's principal ideal theorem (Hauptidealsatz)
s_krull_pit_theorem | theorem | Krull's principal ideal theorem (Hauptidealsatz)
s_kruskal_tree_theorem | theorem | Kruskal's tree theorem
s_kummer_cyclotomic_factorization | theorem | Kummer's theorem on cyclotomic ideal factorization
s_kunen_inconsistency | theorem | Kunen inconsistency theorem
s_kunen_inconsistency_in_L | state | kunen inconsistency in L
s_kurepa_tree | state | Kurepa tree / Kurepa's hypothesis
s_kurepa_tree_in_L | theorem | Kurepa tree exists in L
s_l_adic_cohomology | state | l_adic_cohomology
s_l_adic_galois_representation_of_E | state | l adic galois representation of E
s_l_adic_tate_module | axiom | l adic tate module
s_l_chi0_pole_at_1 | theorem | Pole of L(s,χ₀) at s = 1
s_l_chi0_relation_to_zeta | state | L(s,χ₀) relation to Riemann zeta
s_l_class | state | Hirzebruch L-class
s_l_extension | state | ℓ-extension
s_l_function_central_value | axiom | l function central value
s_l_function_euler_product_local | theorem | Decomposition of L-functions into local zeta integrals
s_l_function_nonvanishing_s1 | theorem | L-function non-vanishing at s = 1
s_l_function_of_modular_form | axiom | L-function of a modular form
s_l_function_of_motive | state | l_function_of_motive
s_l_function_via_hurwitz_zeta | theorem | L(s,χ) as linear combination of Hurwitz zeta functions
s_l_group_functoriality_setup | state | l group functoriality setup
s_l_infinity_not_separable | theorem | L∞ is not separable
s_l_infinity_space | axiom | L-infinity space
s_lagrange_four_square_theorem | theorem | Lagrange's four-square theorem
s_lambda_lemma_extension | state | lambda lemma extension
s_landau_prime_ideal_theorem | theorem | landau_prime_ideal_theorem
s_langlands_l_function | state | Langlands L-function
s_large_cardinal | state | large cardinal
s_large_cardinal_axioms | state | large_cardinal_axioms
s_large_cardinal_consistency_hierarchy | theorem | large cardinal consistency hierarchy
s_lebesgue_measurable_function | state | Lebesgue measurable function
s_lebesgue_measurable_set_in_Rn | axiom | lebesgue measurable set in Rn
s_lebesgue_space_L_p | axiom | lebesgue space L p
s_lebesgue_spaces_L_p_L_q | axiom | lebesgue spaces L p L q
s_lefschetz_number_L_f | state | lefschetz number L f
s_legendre_three_square_theorem | theorem | Legendre's three-square theorem
s_levy_characterization_bm | theorem | Lévy's Characterization of Brownian Motion
s_levy_collapse_model | state | levy collapse model
s_levy_concentration_function | axiom | levy concentration function
s_levy_concentration_function_witness | state | levy concentration function witness
s_levy_continuity_theorem | theorem | Lévy's Continuity Theorem
s_levy_downward_theorem | theorem | Lévy's downward theorem
s_levy_equivalence_theorem | theorem | Lévy's Equivalence Theorem
s_levy_hierarchy | state | Lévy hierarchy (Σ_n/Π_n)
s_levy_inequality | theorem | Lévy's inequality
s_levy_inversion_formula | theorem | Lévy inversion formula
s_levy_ito_decomposition | theorem | Lévy–Itô decomposition
s_levy_khintchine_formula | theorem | Lévy–Khintchine formula
s_levy_khintchine_representation | theorem | Lévy–Khintchine Representation
s_levy_khintchine_triplet | state | Lévy–Khintchine triplet
s_levy_measure_integral_existence | state | levy measure integral existence
s_levy_modulus_continuity | theorem | Lévy Modulus of Continuity for BM
s_levy_process | axiom | Lévy process
s_levy_process_X_t | axiom | levy process X t
s_levy_reflection | theorem | Levy reflection principle
s_levy_reflection_in_L | state | levy reflection in L
s_levy_solovay_theorem | theorem | Lévy–Solovay theorem on indestructibility of large cardinals under small forcing
s_levy_upward_theorem | theorem | Lévy's upward theorem
s_levy_zero_one_law | theorem | Lévy's 0-1 law
s_levys_lemma_on_the_sphere | state | Lévy's lemma on the sphere
s_lil_harris_chain | theorem | Law of the iterated logarithm for Harris chains
s_lil_hartman_wintner | theorem | Law of Iterated Logarithm (Hartman–Wintner)
s_limit_ordinal | state | limit ordinal
s_line_bundle_L_lambda | state | line bundle L lambda
s_linear_form_l_i | axiom | linear form l i
s_liouville_property_recurrent_mc | theorem | Liouville property for recurrent Markov chains
s_littlewood_paley_square_function_theorem | theorem | Littlewood–Paley decomposition
s_lll_algorithm_properties | theorem | lll_algorithm_properties
s_local_boundedness_L_infty | state | local boundedness L infty
s_local_martingale_M_t | axiom | local martingale M t
s_local_property | axiom | Local property of modules
s_local_time | state | Local time of a continuous semimartingale
s_localization_universal_property | theorem | Universal property of localization
s_log_l_series | state | Logarithm of L(s,χ) series
s_log_zeta_bound_near_sigma_1 | state | log ζ(s) bound near σ = 1
s_lovasz_local_lemma_symmetric | theorem | Lovasz Local Lemma (symmetric form)
s_lovasz_theta_ramsey_bound | theorem | Ramsey bound via Lovasz theta function
s_lp_norm_equivalence_with_square_function | state | lp norm equivalence with square function
s_lr_martingale_under_null | state | lr martingale under null
s_macmahon_plane_partition_gf | theorem | MacMahon's plane partition generating function
s_mader_theorem_average_degree | theorem | Mader's theorem (average degree forces topological minors)
s_mahlo_cardinal | state | Mahlo cardinal
s_mansfield_solovay | theorem | Mansfield–Solovay theorem
s_mapping_lemma_spectral_sequences | theorem | Mapping lemma for spectral sequences
s_markov_kernel | axiom | Markov kernel (transition kernel on measurable space)
s_markov_partition_of_attractor | state | markov partition of attractor
s_markov_property | theorem | Markov property
s_markov_property_bm | theorem | Markov property of Brownian motion
s_markov_property_of_groups | axiom | markov property of groups
s_martin_analytic_determinacy | theorem | Martin's theorem: Σ¹₁-determinacy from measurable
s_martin_borel_determinacy | theorem | Martin's Borel determinacy theorem
s_martin_boundary | state | Martin boundary
s_martin_representation_theorem | theorem | Martin representation theorem
s_martin_steel_pd | theorem | Martin–Steel theorem (projective determinacy)
s_martingale | state | Martingale
s_martingale_Lp_convergence | theorem | Martingale Lᵖ convergence theorem
s_martingale_clt | theorem | Martingale central limit theorem
s_martingale_in_initial_time | state | martingale in initial time
s_martingale_problem | axiom | Martingale problem (Stroock–Varadhan)
s_martingale_transform | axiom | Martingale transform
s_martingale_with_bounded_differences | axiom | martingale with bounded differences
s_martins_axiom | axiom | Martin's Axiom (MA)
s_martins_axiom_MA_kappa | axiom | Martin's Axiom MA_κ
s_martins_axiom_MA_omega_1 | axiom | martins axiom MA omega 1
s_matrix_tree | theorem | Matrix-tree theorem
s_matrix_tree_theorem | theorem | Kirchhoff's matrix-tree theorem
s_maximal_cohen_macaulay_module | axiom | Maximal Cohen-Macaulay module
s_maximal_gamma_set_on_M | state | maximal gamma set on M
s_maximal_ideal | axiom | Maximal Ideal
s_maximal_ideal_m_in_k_x_1_x_n | state | Maximal ideal m ⊂ k[x₁,…,xₙ]
s_maximal_ideal_space | state | Maximal ideal space (spectrum) of a Banach algebra
s_maximal_ideals_are_points | state | maximal_ideals_are_points
s_maximum_principle_forcing | theorem | Maximum principle (forcing)
s_mean_square_convergence_fourier | theorem | Mean-square convergence of Fourier series
s_mean_square_density_index_q | state | mean square density index q
s_mean_value_property_for_f | state | mean value property for f
s_mean_value_property_harmonic | theorem | Mean value property for harmonic functions
s_mean_value_property_heat | theorem | Mean value property for the heat equation
s_mean_value_property_on_balls | axiom | mean value property on balls
s_measurable_cardinal_axiom | axiom | measurable cardinal axiom
s_measurable_coefficient_uniform_ellipticity | axiom | measurable coefficient uniform ellipticity
s_measurable_embedding_characterization | theorem | Measurable cardinals and elementary embeddings
s_measurable_function | state | Measurable function
s_measurable_functions_form_algebra | theorem | Measurable functions form an algebra
s_measurable_hilbert_field | state | measurable hilbert field
s_measurable_set | axiom | Measurable Set
s_measurable_set_of_positive_measure | state | measurable set of positive measure
s_measurable_space | axiom | measurable space
s_measurable_subset_of_Rn | axiom | measurable subset of Rn
s_measure_density_lemma_nondivergence | state | measure density lemma nondivergence
s_memoryless_property | theorem | Memoryless property
s_mertens_and_sigma_translations | state | mertens and sigma translations
s_middle_layer_bound_for_antichain | state | middle layer bound for antichain
s_midpoint_preserved_under_reflection | state | midpoint preserved under reflection
s_miller_rabin_correctness | theorem | miller_rabin_correctness
s_miller_rabin_witness | state | miller_rabin_witness
s_minimal_cauchy_filter | state | Minimal Cauchy filter
s_minimizing_property_of_geodesics | theorem | Minimizing property of geodesics
s_mixing_lemma_forcing | theorem | Mixing lemma
s_model_L_of_ZFC_plus_GCH | state | Model L (constructible universe)
s_model_of_ZFC_plus_not_CH | state | Model of ZFC + ¬CH
s_modified_newton_iteration | state | modified newton iteration
s_modified_struve_function_l_nu | state | Modified Struve Function L_nu(z)
s_modularity_theorem | theorem | Modularity theorem (Taylor–Wiles–Breuil–Conrad–Diamond)
s_modularity_theorem_full | theorem | Modularity theorem (full, Breuil–Conrad–Diamond–Taylor)
s_moments_l_functions_conjectural | axiom | Moments of L-functions (conjectural asymptotics)
s_monotone_boolean_function | axiom | Monotone Boolean function
s_monotonicity_lemma_j_holo | theorem | Monotonicity lemma for J-holomorphic curves
s_morley_tree_analysis | state | morley tree analysis
s_moser_isotopy_lemma_relative | theorem | Moser isotopy lemma (relative version)
s_mostowski_absoluteness | theorem | Mostowski absoluteness
s_mostowski_collapse | theorem | Mostowski collapse lemma
s_mostowski_rank_function | theorem | Mostowski rank theorem
s_mu_measurable_function_bourbaki | axiom | Measurable function (Bourbaki, mu-measurable)
s_multivariate_gamma_function | axiom | Multivariate Gamma Function Gamma_m(a)
s_murnaghan_nakayama_rule | theorem | Murnaghan--Nakayama rule
s_n_measurable_bodies_in_Rn | axiom | n measurable bodies in Rn
s_nakayama_lemma | theorem | Nakayama's lemma
s_nakayama_tate_duality | theorem | Nakayama–Tate duality theorem
s_negative_part_V_minus_in_L_n_2 | axiom | negative part V minus in L n 2
s_negative_schwarzian_preserved_under_iteration | state | negative schwarzian preserved under iteration
s_neighborhood_filter | state | Neighborhood filter
s_newton_iteration_of_conjugacies | state | newton iteration of conjugacies
s_newtonian_inverse_square_force | axiom | Newtonian inverse-square force law
s_nil_ideal | axiom | Nil ideal
s_nilpotent_ideal | axiom | Nilpotent ideal
s_nine_lemma_33_lemma | theorem | Nine lemma (3×3 lemma)
s_non_archimedean_absolute_value | axiom | Non-archimedean absolute value
s_nondivergence_elliptic_with_L_infty_coeff | axiom | nondivergence elliptic with L infty coeff
s_nonneg_measurable_function_on_Rn | axiom | nonneg measurable function on Rn
s_nonnegative_submartingale | axiom | nonnegative submartingale
s_nonvanishing_l_functions_at_center | theorem | Nonvanishing results for central L-values
s_norm_of_ideal | axiom | Norm of an ideal N(𝔞)
s_normal_filter | state | Normal filter
s_normal_measure | state | Normal measure
s_normalized_matching_property | state | Normalized matching property
s_normalized_population_martingale_W_n | state | normalized population martingale W n
s_normed_space_with_proper_closed_subspace_Y | axiom | normed space with proper closed subspace Y
s_notion_of_forcing | state | Notion of forcing
s_nowhere_dense_set | axiom | Nowhere dense set
s_object_over_L_with_descent_data | axiom | object over L with descent data
s_off_diagonal_ramsey_bounds | state | Off-diagonal Ramsey bounds
s_omega_1_branch_kills_suslin | state | omega 1 branch kills suslin
s_one_derivative_L_n_over_n_minus_1_bound | state | one derivative L n over n minus 1 bound
s_only_inverse_square_and_harmonic_close_at_first_order | state | only inverse square and harmonic close at first order
s_optional_sigma_algebra | axiom | Optional σ-algebra
s_orbit_dense_in_full_space | state | orbit dense in full space
s_order_property_dichotomy | state | order property dichotomy
s_ordinal_arithmetic | state | Ordinal arithmetic
s_ordinal_arithmetic_below_epsilon_0 | axiom | ordinal arithmetic below epsilon 0
s_ordinal_majorant_sequence_below_epsilon_0 | state | ordinal majorant sequence below epsilon 0
s_ordinal_number | axiom | Ordinal number
s_ordinal_sequence_must_hit_zero | state | ordinal sequence must hit zero
s_p_adic_absolute_value | axiom | p_adic_absolute_value
s_p_adic_l_function | state | p adic l function
s_p_partition_generating_function | state | P-partition generating function
s_padic_absolute_value | axiom | p-adic absolute value
s_painleve_classification_theorem | theorem | Painlevé property and isomonodromy
s_painleve_property | axiom | Painleve Property
s_painleve_property_definition | state | painleve property definition
s_pair_of_sigma_finite_measures_mu_nu | axiom | pair of sigma finite measures mu nu
s_paley_graph_properties | state | Paley graph properties
s_paracompact_partition_unity | theorem | Paracompactness and partitions of unity
s_parameter_ideal | state | Parameter ideal
s_parameter_word_partition_setup | state | parameter word partition setup
s_partial_coloring_lemma_entropy_bucket | state | partial coloring lemma entropy bucket
s_partial_fraction_l_prime_over_l | state | Partial fraction for −L′/L
s_partial_order_for_forcing | state | partial_order_for_forcing
s_partition_calculus | state | Partition calculus (arrow notation)
s_partition_entropy_function | state | partition entropy function
s_partition_function_Z_tau | axiom | partition function Z tau
s_partition_function_depends_only_on_modulus | state | partition function depends only on modulus
s_partition_function_duality_relation | state | partition function duality relation
s_partition_function_graph | state | Partition function of a graph (statistical mechanics)
s_partition_function_polynomial_P_z | state | partition function polynomial P z
s_partition_function_stat_mech | state | Partition Function (Statistical Mechanics) Z
s_partition_generating_function_q_pochhammer | axiom | partition generating function q pochhammer
s_partition_generating_modular | state | partition generating modular
s_partition_lambda | axiom | partition lambda
s_partition_lattice_pi_n | state | Partition lattice Pi_n
s_partition_of_a_set | state | Partition of a set
s_partition_of_an_integer | axiom | partition of an integer
s_partition_of_interval | axiom | Partition of an interval
s_partition_of_unity | state | Partition of unity
s_partition_of_unity_chart_decomposition | state | partition of unity chart decomposition
s_partition_of_unity_presheaf_acyclicity | theorem | Partition of unity argument for presheaves of forms
s_partition_of_unity_smooth | state | Smooth partition of unity
s_partition_regularity | axiom | Partition regularity
s_partition_relation_kappa_to_kappa_2_2 | axiom | partition relation kappa to kappa 2 2
s_partition_size_upper_bound | state | partition size upper bound
s_partition_subordinate_to_expanding | state | partition subordinate to expanding
s_path_lifting_property | theorem | Path lifting property
s_perfect_ideal | axiom | Perfect ideal
s_perfect_ideal_of_height_2 | axiom | perfect ideal of height 2
s_perfect_ideals_unmixed | theorem | Perfect ideals are unmixed
s_perfect_set_property | state | Perfect set property (PSP)
s_perfect_subtree_case | state | perfect subtree case
s_pettis_measurability | theorem | Pettis theorem (weakly measurable = strongly measurable for separable values)
s_phi_reflection_schema_in_L | state | phi reflection schema in L
s_plane_partition | axiom | Plane Partition
s_plus_construction_B_sigma_infty_plus | state | plus construction B sigma infty plus
s_poincare_lemma_compact_support | theorem | Poincaré lemma for compactly supported cohomology
s_poincare_lemma_covector_fields | theorem | Poincare lemma for covector fields
s_poincare_lemma_local_resolution | state | poincare lemma local resolution
s_pointwise_limit_measurable | theorem | Pointwise limit of measurable functions is measurable
s_pointwise_limit_on_dense_set | state | pointwise limit on dense set
s_polygamma_functions | state | Polygamma Functions
s_polygamma_recurrence_relation | theorem | Polygamma Recurrence Relation
s_polygamma_reflection_formula | theorem | Polygamma Reflection Formula
s_positive_square_root | theorem | Positive square root of a positive operator
s_ppartition | state | P-partition
s_predictable_sigma_algebra | axiom | Predictable σ-algebra
s_prewellordering_property | state | Prewellordering property
s_primary_ideal | axiom | Primary ideal
s_prime_ideal | axiom | prime_ideal
s_prime_ideal_chain | axiom | prime ideal chain
s_principal_filter | state | Principal vs non-principal ultrafilter
s_principal_ideal | axiom | principal ideal
s_principal_ideal_domain | axiom | principal ideal domain
s_principal_ideal_theorem_cft | theorem | Principal ideal theorem (Hauptidealsatz, class field theory)
s_product_forcing_lemma | theorem | Product forcing lemma
s_product_sigma_algebra | state | Product σ-algebra
s_projection_iteration_map_T | state | projection iteration map T
s_projective_determinacy | state | projective determinacy
s_projective_hierarchy_proper | theorem | Projective hierarchy is proper
s_proof_ordinal_assignment | state | proof ordinal assignment
s_proof_tree | axiom | proof tree
s_proper_X_with_coherent_sheaf | state | proper X with coherent sheaf
s_proper_action | axiom | Proper action
s_proper_birational_to_normal | state | proper birational to normal
s_proper_cone | axiom | Proper cone
s_proper_equivalence_of_binary_quadratic_forms | axiom | Proper equivalence of binary quadratic forms
s_proper_forcing | state | Proper forcing
s_proper_forcing_axiom | axiom | proper forcing axiom
s_proper_gap | axiom | Proper generalized arithmetic progression
s_proper_holomorphic_mapping_theorem | theorem | Proper holomorphic mapping theorem
s_proper_map | axiom | Proper map
s_proper_morphism | axiom | Proper morphism
s_proper_morphism_finite_type | state | proper morphism finite type
s_proper_smooth_submersion_f_M_to_N | axiom | proper smooth submersion f M to N
s_proper_vertex_coloring | axiom | Proper vertex coloring
s_properness_preserved_CS_iteration | theorem | Properness preserved under CS iteration
s_properties_of_characteristic_functions | state | Properties of characteristic functions
s_properties_of_conditional_expectation | state | Properties of conditional expectation
s_property_b_existence_uniform | theorem | Property B existence for uniform hypergraphs
s_property_of_baire | state | Property of Baire
s_pumping_lemma_regular | theorem | Pumping lemma for regular languages
s_pushout_square_in_spaces | axiom | pushout square in spaces
s_q_gamma_function | state | q-Gamma Function
s_quadratically_convergent_iteration | state | quadratically convergent iteration
s_quillen_suslin_theorem | theorem | Quillen–Suslin theorem (Serre's conjecture)
s_quintic_polynomial | state | Generic quintic polynomial
s_quotient_by_maximal_is_field | theorem | Quotient by Maximal Ideal is Field
s_quotient_by_prime_is_domain | theorem | Quotient by Prime Ideal is Integral Domain
s_rademacher_exact_formula_partition | theorem | Rademacher exact formula for p(n)
s_radical_equals_intersection_of_primes_containing_ideal | theorem | Radical equals intersection of primes containing ideal
s_radical_ideal | state | radical_ideal
s_radical_of_an_ideal | state | Radical of an Ideal
s_rado_partition_regularity | theorem | Rado's theorem (partition regularity)
s_radon_partition_giving_common_intersection | state | radon partition giving common intersection
s_radon_partition_step | state | radon partition step
s_rainbow_partition_problem | state | rainbow partition problem
s_ramanujan_partition_congruences | theorem | Ramanujan's congruences
s_ramsey_cardinal | state | Ramsey cardinal
s_ramsey_lower_bound_alteration | theorem | Ramsey lower bound via alteration
s_ramsey_multiplicity | state | Ramsey multiplicity
s_ramsey_number | axiom | Ramsey number R(r, s)
s_ramsey_number_recurrence_R_r_s | state | ramsey number recurrence R r s
s_ramsey_theorem_diestel | theorem | Ramsey's theorem (finite, graph version)
s_ramsey_theorem_finite | theorem | Ramsey's theorem (finite version)
s_ramsey_theorem_hypergraph | theorem | Ramsey's theorem (hypergraph version)
s_ramsey_theorem_infinite | theorem | Infinite Ramsey theorem
s_ramsey_theorem_infinite_diestel | theorem | Infinite Ramsey theorem
s_ramsey_theorem_multicolor | theorem | Ramsey's theorem (multicolor version)
s_ramsey_upper_bound_lll | state | Off-diagonal Ramsey bound via LLL
s_random_maximal_chain_on_boolean_lattice | state | random maximal chain on boolean lattice
s_random_real_extension_over_measurable | state | random real extension over measurable
s_random_real_forcing | theorem | Solovay random real forcing
s_random_variable | axiom | Random variable
s_rankin_selberg_l_function | axiom | Rankin–Selberg L-function
s_rate_measure_lambda_on_sigma_finite_space | axiom | rate measure lambda on sigma finite space
s_ratio_limit_theorem_chung_erdos_orey | theorem | Ratio limit theorem (Chung-Erdős-Orey form)
s_rayleigh_quotient_with_extremal_property | state | rayleigh quotient with extremal property
s_re_index_set_property | state | re index set property
s_real_subalgebra_dense | state | real subalgebra dense
s_real_valued_measurable_cardinal | axiom | real valued measurable cardinal
s_reciprocal_gamma_entire | state | Reciprocal Gamma as Entire Function
s_recurrence_is_class_property | theorem | Recurrence is a class property
s_recursion_tree_decomposition | state | recursion tree decomposition
s_recursive_binary_tree_T | state | recursive binary tree T
s_recursive_ordinal | axiom | recursive ordinal
s_reduced_suspension_sigma_X | axiom | reduced suspension sigma X
s_reduction_of_an_ideal | state | Reduction of an ideal
s_reduction_to_identity_after_n_reflections | state | reduction to identity after n reflections
s_reference_sigma_finite_measure | axiom | reference sigma finite measure
s_reflection_extension_in_each_chart | state | reflection extension in each chart
s_reflection_generators | state | reflection generators
s_reflection_in_L | theorem | Reflection theorem in L
s_reflection_of_limits | axiom | Reflection of limits
s_reflection_principle | theorem | Reflection principle
s_reflection_principle_bm | theorem | Reflection principle for Brownian motion
s_reflection_s_alpha | state | Reflection s_α in a root system
s_reflection_schema_for_finite_subtheory | state | reflection schema for finite subtheory
s_regressive_finite_ramsey_statement | state | regressive finite ramsey statement
s_regressive_function_on_stationary_set | axiom | regressive function on stationary set
s_regular_cardinal | axiom | Regular cardinal
s_regular_cardinal_arithmetic | axiom | regular cardinal arithmetic
s_regular_uncountable_cardinal_kappa | axiom | regular uncountable cardinal kappa
s_regularity_partition | state | regularity partition
s_relations_collapse_to_14 | state | relations collapse to 14
s_relative_constructibility_L_A | state | Relative constructibility L[A]
s_relatively_large_ramsey_statement | state | relatively large ramsey statement
s_remmert_proper_mapping_theorem | theorem | Remmert proper mapping theorem
s_replete_ideal | axiom | Replete ideal (Arakelov ideal)
s_rescaled_iteration_on_cone | state | rescaled iteration on cone
s_right_continuous_martingale | axiom | Right-continuous martingale
s_root_decomposition_properties | theorem | Properties of the root space decomposition
s_running_maxima_M_n | state | running maxima M n
s_sa_part_dense_via_functional_calculus | state | sa part dense via functional calculus
s_sacks_density_theorem | theorem | Sacks density theorem
s_sacks_jump_inversion | theorem | Sacks jump inversion theorem
s_sacks_splitting_theorem | theorem | Sacks splitting theorem
s_sat_boolean_satisfiability | state | SAT (Boolean satisfiability)
s_saturated_ultrapowers | state | saturated ultrapowers
s_scale_property | state | Scale property
s_schrodinger_operator_L_with_potential_u | axiom | schrodinger operator L with potential u
s_schur_property_l1 | theorem | Schur property of ℓ¹
s_schur_ramsey | theorem | Schur's theorem (Ramsey)
s_schurs_lemma_2 | theorem | schurs_lemma
s_schwarz_reflection_principle | theorem | Schwarz reflection principle
s_scott_theorem_V_not_L | theorem | Scott's theorem (no measurable cardinal in L)
s_second_difference_subsolution_property | state | second difference subsolution property
s_second_isomorphism_theorem | theorem | Second isomorphism theorem (diamond)
s_second_moment_l_functions_characters | theorem | Second moment of L-functions over characters
s_second_order_martingale | state | second order martingale
s_selberg_erdos_elementary_pnt | theorem | Selberg–Erdős elementary proof of PNT
s_semimartingale | axiom | Semimartingale
s_semisimple_decomposition_into_simples | theorem | Decomposition of semisimple Lie algebras into simple ideals
s_semisimple_direct_sum_of_simples | theorem | Semisimple Lie algebra is a direct sum of simple ideals
s_sensitivity_boolean | axiom | Sensitivity of a Boolean function
s_separation_properties_tvs | theorem | Separation properties of topological vector spaces
s_sequence_of_connections_with_L_2_bounded_curvature | axiom | sequence of connections with L 2 bounded curvature
s_sequence_of_measurable_events | axiom | sequence of measurable events
s_sequence_of_uniformly_absolutely_continuous_measures | axiom | sequence of uniformly absolutely continuous measures
s_shannon_entropy_of_partition | state | Shannon entropy of a partition
s_shannon_mcmillan_breiman | theorem | Shannon-McMillan-Breiman theorem
s_sharps_analytic_determinacy_equivalence | state | Sharps and analytic determinacy equivalence
s_sheaf_cohomology_of_L_lambda | state | sheaf cohomology of L lambda
s_sheaf_property_distributions | theorem | Sheaf property of distributions
s_shelah_inaccessible_necessary | theorem | Inaccessible necessary for all sets Lebesgue measurable (Shelah)
s_shoenfield_absoluteness | theorem | Shoenfield absoluteness theorem
s_shoenfield_tree_with_absolute_wellfoundedness | state | shoenfield tree with absolute wellfoundedness
s_siegel_lemma_l_function_products | theorem | Siegel's lemma on L-function products
s_siegel_theorem_l_functions | theorem | Siegel's theorem on L(1,χ)
s_sigma_1_1_as_wellfoundedness | state | sigma 1 1 as wellfoundedness
s_sigma_1_2_as_tree_projection | state | sigma 1 2 as tree projection
s_sigma_1_2_formula | state | sigma 1 2 formula
s_sigma_1_2_normal_form | state | sigma 1 2 normal form
s_sigma_1_2_set_of_reals | axiom | sigma 1 2 set of reals
s_sigma_algebra | axiom | σ-algebra
s_sigma_algebra_generated | axiom | sigma algebra generated
s_sigma_algebra_generated_by_rv | state | σ-algebra generated by a random variable
s_sigma_algebra_of_measurable_sets | state | sigma algebra of measurable sets
s_sigma_compact_space | axiom | Sigma-compact space
s_sigma_discrete_basis_present | state | sigma discrete basis present
s_sigma_finite_measure_space | axiom | sigma finite measure space
s_sigma_finite_signed_measure | axiom | sigma finite signed measure
s_sigma_infty_CP_infty_bott_inverted | state | sigma infty CP infty bott inverted
s_sigma_locally_finite_basis | axiom | sigma locally finite basis
s_sigma_locally_finite_basis_present | state | sigma locally finite basis present
s_sigma_multiplicative | state | sigma multiplicative
s_sigma_n_projectum | state | Σ_n-projectum ρ_n
s_signed_measure_on_measurable_space | axiom | signed measure on measurable space
s_silver_indiscernibles | state | Silver indiscernibles
s_silver_indiscernibles_in_L | state | silver indiscernibles in L
s_silver_indiscernibles_theorem | theorem | Silver indiscernibles theorem
s_silver_singular_cardinals_theorem | theorem | Silver's theorem on singular cardinals
s_silver_theorem | theorem | Silver's theorem
s_simple_reflections_generate_weyl_group | theorem | Simple reflections generate the Weyl group
s_simply_connected_proper_domain_in_C | axiom | Simply connected proper domain in ℂ
s_singular_cardinal | axiom | Singular cardinal
s_singular_cardinal_hypothesis | state | Singular Cardinal Hypothesis (SCH)
s_singular_cardinal_kappa_of_uncountable_cofinality | axiom | singular cardinal kappa of uncountable cofinality
s_singular_plus_absolutely_continuous_split | state | singular plus absolutely continuous split
s_sle_kappa_driver | state | sle kappa driver
s_small_forcing_P_below_kappa | axiom | small forcing P below kappa
s_smooth_functions_dense_in_W1p | state | smooth functions dense in W1p
s_smoothing_property_heat | theorem | Smoothing property of the heat equation
s_snake_lemma_applied_to_homology | state | snake lemma applied to homology
s_solovay_RVM_theorem | theorem | Solovay's theorem on real-valued measurable cardinals
s_solovay_model | theorem | Solovay's model (every set Lebesgue-measurable)
s_solovay_stationary_splitting | theorem | Solovay's stationary splitting theorem
s_solvable_action_on_proper | state | solvable action on proper
s_some_iterates_must_overlap_in_measure | state | some iterates must overlap in measure
s_space_time_L_q_t_L_r_x_bound | state | space time L q t L r x bound
s_spanning_tree | axiom | Spanning tree
s_sparse_ramsey_theorem | theorem | Rodl-Rucinski sparse Ramsey theorem
s_special_aronszajn_tree | state | Special Aronszajn tree
s_spectral_decomposition_l2_gamma_h | theorem | Spectral decomposition of L²(Γ\H)
s_spectral_sequence_collapse | state | Collapsing of a spectral sequence
s_spectral_sequence_filtered_complex | state | Spectral sequence of a filtered complex
s_spencer_six_sigma_theorem | theorem | Spencer's six standard deviations
s_splitting_lemma_modules | theorem | Splitting Lemma for Modules
s_square_function_S_f | state | square function S f
s_square_holds_in_L | theorem | □_κ holds in L (Jensen)
s_square_matrix_over_ring | axiom | square matrix over ring
s_square_matrix_with_char_poly | state | square matrix with char poly
s_square_principle | axiom | Square principle □_κ (Jensen)
s_square_step_set | axiom | square step set
s_stanley_hook_content_formula_plane_partitions | theorem | Stanley's hook content formula for column-strict plane partitions
s_state_space_collapse_petite | theorem | Compact sets are petite for T-chains
s_stationary_GCH_carrier | state | stationary GCH carrier
s_stationary_distribution | state | stationary distribution
s_stationary_increments_process | axiom | Stationary increments
s_stationary_phase_method | theorem | stationary phase method
s_stationary_phase_point | state | stationary phase point
s_stationary_process | axiom | Stationary process
s_stationary_renewal_coupling | state | stationary renewal coupling
s_stationary_subset_of_kappa | axiom | stationary subset of kappa
s_stein_lemma_gaussian | theorem | Stein's Lemma (Gaussian integration by parts)
s_stern_brocot_tree | axiom | Stern–Brocot tree
s_stone_cech_universal_property | theorem | Universal property of Stone-Čech compactification
s_stopped_sigma_algebra | state | Stopped σ-algebra
s_stopped_submartingale_at_tau | state | stopped submartingale at tau
s_strassen_functional_lil | theorem | Functional Law of the Iterated Logarithm (Strassen)
s_strong_exchange_property | theorem | Strong exchange property
s_strong_feller_property | axiom | Strong Feller property
s_strong_markov_property_bm | theorem | Strong Markov property of Brownian motion
s_strong_markov_property_mc | theorem | Strong Markov property for Markov chains
s_strong_markov_property_rw | theorem | Strong Markov property for random walks
s_strong_ramsey_independence | theorem | Ramsey-type Paris–Harrington-style independence (general PA-unprovable)
s_strong_subtree_template | state | strong subtree template
s_strong_unique_continuation_property | theorem | Strong unique continuation property
s_strongly_compact_cardinal | state | Strongly compact cardinal
s_strongly_measurable_function | axiom | Strongly measurable function
s_structural_property_loss | state | structural property loss
s_submartingale | axiom | Submartingale
s_submartingale_X_n | axiom | submartingale X n
s_successor_cardinals_regular | theorem | Successor cardinals are regular
s_successor_ordinal | state | successor ordinal
s_sunflower_lemma_erdsko | theorem | Sunflower lemma (Erdős-Ko)
s_supercompact_cardinal | state | supercompact cardinal
s_supermartingale | state | supermartingale
s_supermartingale_convergence_for_V_n | state | supermartingale convergence for V n
s_suslin_problem | state | Suslin's problem (Suslin Hypothesis)
s_suslin_space | axiom | Suslin space (analytic space)
s_suslin_tree | state | Suslin tree
s_suslin_tree_line_equivalence | theorem | Equivalence of Suslin tree and Suslin line
s_symbolic_power_of_a_prime | axiom | Symbolic power of a prime ideal
s_symmetric_groups_Sigma_n | axiom | symmetric groups Sigma n
s_symmetric_power_l_functions | state | symmetric power l functions
s_symmetric_square_l_function | axiom | Symmetric square L-function L(sym²f, s)
s_t_intersecting_family_property | axiom | t intersecting family property
s_tail_sigma_algebra | axiom | Tail σ-algebra
s_taniyama_shimura_conjecture | state | taniyama_shimura_conjecture
s_teichmuller_pullback_map_sigma_f | state | teichmuller pullback map sigma f
s_ten_martini_theorem | theorem | Avila–Damanik almost Mathieu spectrum (Ten Martini Problem)
s_tensor_product_universal_property | theorem | Tensor product universal property
s_theorema_egregium | theorem | Theorema Egregium
s_three_nonneg_measurable_functions_with_log_concave_constraint | axiom | three nonneg measurable functions with log concave constraint
s_three_property_axiom_definition | state | three property axiom definition
s_three_term_AP_free_property | axiom | three term AP free property
s_threshold_phenomenon | theorem | Threshold phenomenon for monotone properties
s_tournament_domination_bound | theorem | Tournament dominating set bound
s_tower_property | theorem | Tower property of conditional expectation
s_trace_on_smooth_dense_subset | state | trace on smooth dense subset
s_tracial_ultrapower_target | state | tracial ultrapower target
s_trajectory_partition_of_A | state | trajectory partition of A
s_tree_branch_level_height | state | Branch, level, and height of a tree
s_tree_decomposition | axiom | Tree-decomposition
s_tree_graph | axiom | Tree (graph theory)
s_tree_of_height_omega_1 | axiom | tree of height omega 1
s_tree_of_models_decomposition | state | tree of models decomposition
s_tree_on_a_set_body | state | Tree on a set and its body [T]
s_tree_property_for_kappa | state | tree property for kappa
s_tree_representation_of_analytic_set | state | tree representation of analytic set
s_tree_set_theoretic | axiom | Tree (set-theoretic)
s_tree_structured_lz_parsing | state | LZ78 phrase / dictionary tree
s_tree_width | axiom | Tree-width
s_tree_width_decomposition | state | Tree-width decomposition
s_tree_width_duality | theorem | Tree-width duality theorem (Seymour–Thomas)
s_triangle_free_graph_property | axiom | triangle free graph property
s_trichotomy_of_cardinals | theorem | Trichotomy of cardinals
s_twisted_l_function | axiom | Twisted L-function L(f⊗χ, s)
s_two_cardinal_model_M | state | two cardinal model M
s_two_kappa_sized_models_distinct | state | two kappa sized models distinct
s_two_nonempty_measurable_subsets_of_Rn | axiom | two nonempty measurable subsets of Rn
s_two_point_interpolation_property | state | two point interpolation property
s_two_real_series_one_absolutely_convergent | axiom | two real series one absolutely convergent
s_two_square_theorem_via_theta | theorem | Two-square theorem via theta functions
s_type_class_partition | state | type class partition
s_type_of_cm_ring | state | Type of a Cohen-Macaulay ring
s_typical_set_properties | theorem | Properties of the typical set
s_ultrafilter | state | ultrafilter
s_ultrafilter_limit_in_product | state | Ultrafilter limit in ∏Xᵢ
s_ultrafilter_on_index_set | axiom | ultrafilter on index set
s_ultrafilter_on_variable_words | state | ultrafilter on variable words
s_ultrafilter_spectrum_Spec_B | state | ultrafilter spectrum Spec B
s_ultrapower_embedding_j | state | ultrapower embedding j
s_ultrapower_of_hyperfinite_R_omega | axiom | ultrapower of hyperfinite R omega
s_ultrapowers_M_U_N_U | state | ultrapowers M U N U
s_uncountable_partition_target | state | uncountable partition target
s_uniform_integrability_of_Lp_martingale | state | uniform integrability of Lp martingale
s_uniformly_integrable_martingale | axiom | uniformly integrable martingale
s_unique_factorization_ideals_dedekind | theorem | Unique factorization of ideals in Dedekind domains
s_unique_irreducible_quotient_L_lambda | state | unique irreducible quotient L lambda
s_universal_property_completion | theorem | Universal property of completion
s_universal_property_enveloping_algebra | theorem | Universal property of the enveloping algebra
s_universal_property_of_free_groups | theorem | Universal property of free groups
s_universal_property_of_the_exterior_algebra | theorem | Universal property of the exterior algebra
s_universal_property_of_the_symmetric_algebra | theorem | Universal property of the symmetric algebra
s_universal_property_of_the_tensor_algebra | theorem | Universal property of the tensor algebra
s_universal_property_product_topology | theorem | Universal property of product topology
s_universal_property_quotient_topology | theorem | Universal property of quotient topology
s_universal_property_via_hom | state | universal property via hom
s_v_l_axiom_of_constructibility | state | V = L (axiom of constructibility)
s_valuation_ring_of_an_absolute_value | state | Valuation ring of an absolute value
s_valuative_criterion_properness | theorem | Valuative criterion of properness
s_vanishing_ideal | state | vanishing_ideal
s_vaught_two_cardinal | theorem | Vaught's two-cardinal theorem
s_verma_module_M_lambda | state | verma module M lambda
s_vertex_coloring_proper | axiom | Proper vertex coloring
s_vitali_nonmeasurable_set | state | Non-Lebesgue-measurable set (Vitali set)
s_wadge_hierarchy_theorem | theorem | Wadge hierarchy / antichain structure
s_weakly_compact_cardinal | state | Weakly compact cardinal
s_weakly_compact_tree_property | theorem | Tree property characterization of weak compactness
s_weierstrass_product_for_completed_l_function | state | Weierstrass product for completed L-function
s_weierstrass_sigma_function | axiom | Weierstrass Sigma Function sigma(z)
s_weil_differential_repartition | axiom | Weil differential (repartition)
s_well_founded_tree_rank | state | Well-founded tree and its rank
s_wellfounded_tree_T_x | state | wellfounded tree T x
s_wellfoundedness_absolute_for_transitive_models | state | wellfoundedness absolute for transitive models
s_whittaker_function_m_kappa_mu | state | Whittaker Function M_{kappa,mu}(z)
s_whittaker_function_w_kappa_mu | state | Whittaker Function W_{kappa,mu}(z)
s_wiener_inversion_theorem | theorem | Wiener's theorem on Fourier series (absolute convergence)
s_wiener_lemma_katznelson | theorem | Wiener's lemma (absolutely convergent Fourier series)
s_woodin_cardinal | state | Woodin cardinal
s_z_l_extension | state | ℤ_ℓ-extension
s_zero_free_region_l_functions | theorem | Classical zero-free region for L-functions
s_zeta_product_sigma_series | state | ζ(s)ζ(s−1) = ∑ σ(n)/nˢ
s_zfc_axioms | axiom | ZFC axioms
s_zfc_axioms_2 | axiom | zfc_axioms
s_zonal_polynomials | axiom | Zonal Polynomials Z_kappa(T)
s_zorns_lemma_implies_maximal_ideals_exist | theorem | Zorn's lemma implies maximal ideals exist
s_zygmund_L_log_L_theorem | theorem | Zygmund's L log L theorem for conjugate function
t_absoluteness | technique | Absoluteness
t_arnoldi_iteration | technique | Arnoldi Iteration
t_azuma_hoeffding_technique | technique | Azuma-Hoeffding technique
t_boolean_truth_value | technique | Boolean truth value ‖φ‖
t_canonical_names | technique | Canonical names (x̌, Ġ)
t_cauchy_filter_completion_construction | technique | Cauchy filter completion construction
t_chain_partition | technique | Chain partition technique
t_cofinal_subnet_extraction | technique | Cofinal subnet extraction
t_cohen_forcing | technique | Cohen forcing
t_cohen_macaulay_approximation | technique | Cohen-Macaulay approximation
t_comma_category_construction | technique | Comma category construction technique
t_contraction_iteration_technique | technique | Contraction iteration technique
t_countable_support_iteration | technique | Countable-support iteration
t_duality_lemma_random_walk | technique | Duality lemma for random walks
t_durfee_square_decomposition | technique | Durfee square decomposition
t_edge_exposure_martingale | technique | Edge exposure martingale
t_ehrenfeucht_mostowski_models | technique | Ehrenfeucht–Mostowski models
t_exhaustion_sigma_finite | technique | Exhaustion technique (σ-finite decomposition)
t_fatou_lemma_technique | technique | Fatou's lemma technique
t_filter_argument_compactness | technique | Filter argument for compactness
t_finite_support_iteration | technique | Finite-support iteration
t_force_independence | technique | Force independence
t_forcing_technique | technique | forcing technique
t_fourier_analysis_boolean | technique | Fourier analysis on the Boolean cube
t_gamma_function_technique | technique | Gamma function technique
t_generic_chaining | technique | generic chaining
t_generic_point_argument | technique | Generic point argument
t_gluing_via_partition_of_unity | technique | Smooth maps into Euclidean space (gluing lemma)
t_graph_property_testing | technique | Graph property testing
t_help_lemma | technique | HELP lemma (homotopy extension and lifting property)
t_homogeneous_tree | technique | Homogeneously Suslin set / homogeneous tree
t_horseshoe_lemma_application_dimension_shifting | technique | Horseshoe lemma application in dimension shifting
t_horseshoe_lemma_construction | technique | Horseshoe lemma construction
t_hua_iterative_squaring | technique | Hua’s lemma proof by iterative squaring
t_ideal_arithmetic | technique | ideal_arithmetic
t_ideal_norm_reduction | technique | Ideal norm reduction
t_inverse_iteration | technique | Inverse Iteration
t_iterated_forcing | technique | iterated forcing
t_iterated_ultrapowers | technique | Iterated ultrapowers
t_kalman_filter | technique | Kalman filter
t_lanczos_iteration | technique | Lanczos Iteration
t_levy_collapse | technique | Lévy collapse Coll(ω,κ)
t_lovasz_local_lemma_technique | technique | Lovasz Local Lemma technique
t_major_arc_approximation_via_l_functions | technique | Major arc approximation via L-functions
t_martingale_convergence_technique | technique | Martingale technique for proving convergence
t_martingale_method_cinlar | technique | Martingale method
t_miller_rabin_test | technique | miller_rabin_test
t_moser_iteration | technique | Moser iteration technique
t_nakayamas_lemma_argument | technique | Nakayama's lemma argument
t_nice_names | technique | Nice names
t_p_names | technique | P-names
t_partition_of_unity_technique | technique | Partition of unity technique
t_picard_iteration | technique | picard_iteration
t_polyhedral_geometry_of_partitions | technique | Polyhedral geometry of partitions
t_power_iteration | technique | Power Iteration
t_product_all_l_functions_mod_m | technique | Product of all L-functions mod m
t_rayleigh_quotient_iteration | technique | Rayleigh Quotient Iteration
t_reflection_method | technique | Reflection method for Sobolev extension
t_reflection_principle_andre | technique | Reflection principle (André)
t_shoenfield_tree | technique | Shoenfield tree
t_simultaneous_iteration | technique | Simultaneous Iteration (Subspace Iteration)
t_smooth_partition_of_unity | technique | Smooth partition of unity
t_solovay_model_construction | technique | Solovay's model construction via Lévy collapse
t_square_sieve | technique | Square sieve (Heath-Brown)
t_stationary_phase | technique | Stationary phase method
t_stationary_phase_method | technique | Method of Stationary Phase
t_stationary_scattering_theory | technique | Stationary scattering theory
t_stepping_up_ramsey | technique | Stepping-up technique
t_suslin_operation | technique | Suslin operation 𝒜
t_tree_decomposition_technique | technique | Tree-decomposition dynamic programming
t_tube_lemma_argument | technique | Tube lemma argument
t_two_step_iteration | technique | Two-step iteration P∗Q̇
t_ultrapower_Ult_V_U | technique | Ultrapower Ult(V,U)
t_universal_property_argument | technique | Universal property argument
t_verma_module_induction | technique | Verma module construction by parabolic induction
t_vertex_exposure_martingale | technique | Vertex exposure martingale