s_transitive_closure | state | Transitive closure TC(x)
s_burali_forti_paradox | theorem | Burali-Forti paradox
s_ordinal_arithmetic | state | Ordinal arithmetic
s_cantor_normal_form | theorem | Cantor normal form
s_epsilon_numbers | state | Epsilon numbers (ε-numbers)
s_order_type | state | Order type
s_rank_function | state | Rank function
t_epsilon_induction | technique | ∈-induction (Foundation induction)
s_well_founded_relation | axiom | Well-founded relation
t_well_founded_recursion | technique | Well-founded recursion
s_hereditarily_small_sets_H_kappa | state | Hereditarily small sets H(κ)
s_aleph_function | state | Aleph function ℵ_α
s_initial_ordinal | state | Initial ordinal
s_cardinal_arithmetic | state | Cardinal arithmetic
s_hessenberg_kappa_squared | theorem | Hessenberg's theorem (κ²=κ)
s_godel_pairing_function | state | Gödel pairing function
s_cofinality | state | Cofinality cf(α)
s_regular_cardinal | axiom | Regular cardinal
s_singular_cardinal | axiom | Singular cardinal
s_successor_cardinals_regular | theorem | Successor cardinals are regular
s_continuum_function | state | Continuum function
s_hausdorff_formula | theorem | Hausdorff formula
s_gimel_function | state | Gimel function ℷ(κ)
s_beth_function | state | Beth function ℶ_α
s_generalized_continuum_hypothesis | state | Generalized Continuum Hypothesis (GCH)
s_tukey_lemma | theorem | Tukey's lemma
s_trichotomy_of_cardinals | theorem | Trichotomy of cardinals
s_ideal_set_theory | axiom | Ideal (set-theoretic)
s_kappa_complete_filter | axiom | κ-complete filter
s_principal_filter | state | Principal vs non-principal ultrafilter
s_boolean_prime_ideal_theorem | theorem | Boolean Prime Ideal Theorem
s_complete_boolean_algebra | axiom | Complete Boolean algebra
s_regular_open_algebra | state | Regular open algebra RO(P)
s_club_set | state | Closed unbounded (club) set
s_club_filter | state | Club filter
s_normal_filter | state | Normal filter
s_club_intersection_theorem | theorem | Intersection of clubs is club
s_tree_set_theoretic | axiom | Tree (set-theoretic)
s_tree_branch_level_height | state | Branch, level, and height of a tree
s_aronszajn_tree | state | Aronszajn tree
s_aronszajn_tree_existence | theorem | Existence of an Aronszajn tree
s_suslin_tree | state | Suslin tree
s_suslin_problem | state | Suslin's problem (Suslin Hypothesis)
s_suslin_tree_line_equivalence | theorem | Equivalence of Suslin tree and Suslin line
s_kurepa_tree | state | Kurepa tree / Kurepa's hypothesis
s_special_aronszajn_tree | state | Special Aronszajn tree
s_partition_calculus | state | Partition calculus (arrow notation)
s_square_principle | axiom | Square principle □_κ (Jensen)
s_club_principle | state | Club principle ♣
s_diamond_implies_ch | theorem | ◊ implies CH
s_singular_cardinal_hypothesis | state | Singular Cardinal Hypothesis (SCH)
s_levy_hierarchy | state | Lévy hierarchy (Σ_n/Π_n)
t_absoluteness | technique | Absoluteness
t_elementary_submodel_method | technique | Elementary submodel method
t_skolem_hull | technique | Skolem functions / Skolem hull
t_godel_operations | technique | Gödel operations 𝒢₁–𝒢₁₀
s_constructible_wellordering | state | Constructible well-ordering <_L
s_ac_in_L | theorem | AC holds in L
s_relative_constructibility_L_A | state | Relative constructibility L[A]
s_L_of_A | state | Constructible closure L(A)
s_diamond_holds_in_L | theorem | ◊ holds in L (Jensen)
s_square_holds_in_L | theorem | □_κ holds in L (Jensen)
s_kurepa_tree_in_L | theorem | Kurepa tree exists in L
t_rudimentary_functions | technique | Rudimentary functions
s_jensen_J_hierarchy | state | Jensen J-hierarchy J_α
s_sigma_n_projectum | state | Σ_n-projectum ρ_n
t_fine_structural_condensation | technique | Fine-structural condensation
s_silver_indiscernibles | state | Silver indiscernibles
s_zero_sharp_implies_V_not_L | theorem | 0# exists implies V≠L
s_covering_implies_SCH | theorem | Covering lemma implies SCH
s_notion_of_forcing | state | Notion of forcing
s_dense_predense | state | Dense and predense sets
s_compatible_conditions | state | Compatible and incompatible conditions
s_rasiowa_sikorski_lemma | theorem | Rasiowa–Sikorski lemma
t_p_names | technique | P-names
t_canonical_names | technique | Canonical names (x̌, Ġ)
s_forcing_relation | state | Forcing relation p⊩φ
s_definability_lemma_forcing | theorem | Definability lemma (forcing)
s_truth_lemma | theorem | Truth lemma
s_forcing_theorem | theorem | Forcing theorem (fundamental)
s_ground_model_definability | theorem | Ground model definability
t_separative_quotient | technique | Separativity / separative quotient
t_cohen_forcing | technique | Cohen forcing
s_ccc_forcing | state | Countable chain condition (ccc)
s_ccc_preserves_cardinals | theorem | ccc forcing preserves cardinals
s_cohen_forcing_is_ccc | theorem | Cohen forcing is ccc
t_nice_names | technique | Nice names
s_con_zfc_not_ch_cohen | theorem | Con(ZFC)⟹Con(ZFC+¬CH) (Cohen)
s_boolean_valued_universe | state | Boolean-valued universe V^B
t_boolean_truth_value | technique | Boolean truth value ‖φ‖
s_mixing_lemma_forcing | theorem | Mixing lemma
s_maximum_principle_forcing | theorem | Maximum principle (forcing)
t_levy_collapse | technique | Lévy collapse Coll(ω,κ)
s_kappa_closed_forcing | state | <κ-closed forcing
s_closed_forcing_adds_no_sequences | theorem | <κ-closed forcing adds no new <κ-sequences
s_kappa_cc_knaster | state | κ-cc / κ-Knaster
s_kappa_cc_preserves_cardinals | theorem | κ-cc forcing preserves cardinals ≥κ
s_product_forcing_lemma | theorem | Product forcing lemma
t_two_step_iteration | technique | Two-step iteration P∗Q̇
s_martins_axiom_MA_kappa | axiom | Martin's Axiom MA_κ
s_martins_axiom | axiom | Martin's Axiom (MA)
s_MA_aleph0_theorem | theorem | MA_{ℵ₀} is a theorem of ZFC
s_con_MA_not_CH | theorem | Con(MA+¬CH) (Solovay–Tennenbaum)
t_finite_support_iteration | technique | Finite-support iteration
s_fs_iteration_ccc | theorem | FS iteration of ccc is ccc
s_MA_aleph1_negates_CH | theorem | MA_{ℵ₁} implies ¬CH
s_con_SH | theorem | Con(SH) (Solovay–Tennenbaum)
s_MA_measure_category | theorem | MA and additivity of measure/category
t_countable_support_iteration | technique | Countable-support iteration
s_properness_preserved_CS_iteration | theorem | Properness preserved under CS iteration
s_mahlo_cardinal | state | Mahlo cardinal
s_weakly_compact_cardinal | state | Weakly compact cardinal
s_weakly_compact_tree_property | theorem | Tree property characterization of weak compactness
s_normal_measure | state | Normal measure
t_ultrapower_Ult_V_U | technique | Ultrapower Ult(V,U)
s_measurable_embedding_characterization | theorem | Measurable cardinals and elementary embeddings
t_iterated_ultrapowers | technique | Iterated ultrapowers
s_ramsey_cardinal | state | Ramsey cardinal
s_erdos_cardinal | state | Erdős cardinal κ→(α)^{<ω}
t_ehrenfeucht_mostowski_models | technique | Ehrenfeucht–Mostowski models
s_erdos_implies_zero_sharp | theorem | κ→(ω₁)^{<ω} implies 0# exists
s_strongly_compact_cardinal | state | Strongly compact cardinal
s_huge_cardinal | state | Huge cardinal
t_extenders | technique | Extenders
s_vopenka_principle | axiom | Vopěnka's principle
s_proper_forcing | state | Proper forcing
s_cantor_space | state | Cantor space 2^ω
s_baire_space_irrationals | theorem | Baire space homeomorphic to the irrationals
s_universality_of_baire_space | theorem | Universality of Baire space
s_tree_on_a_set_body | state | Tree on a set and its body [T]
s_well_founded_tree_rank | state | Well-founded tree and its rank
s_borel_hierarchy | state | Borel hierarchy (Σ⁰_α,Π⁰_α,Δ⁰_α)
t_borel_codes | technique | Borel codes
s_property_of_baire | state | Property of Baire
t_suslin_operation | technique | Suslin operation 𝒜
s_coanalytic_set | state | Coanalytic set Π¹₁
s_cantor_bendixson_rank | technique | Cantor–Bendixson derivative and rank
s_perfect_set_property | state | Perfect set property (PSP)
s_analytic_psp | theorem | Analytic sets have the perfect set property
s_analytic_measurable | theorem | Analytic sets are Lebesgue measurable
s_analytic_baire_property | theorem | Analytic sets have the Baire property
s_universal_analytic_set | state | Universal analytic set
t_pi11_norm | technique | Π¹₁ norm / rank
s_boundedness_theorem | theorem | Σ¹₁-boundedness theorem
s_projective_hierarchy | state | Projective hierarchy (Σ¹_n,Π¹_n,Δ¹_n)
s_projective_hierarchy_proper | theorem | Projective hierarchy is proper
s_uniformization | state | Uniformization
s_sigma2_uniformization | theorem | Σ¹₂-uniformization (Novikov–Kondô–Addison)
s_prewellordering_property | state | Prewellordering property
s_scale_property | state | Scale property
s_periodicity_theorems | theorem | Periodicity theorems (Moschovakis)
t_shoenfield_tree | technique | Shoenfield tree
s_sigma2_wellordering_in_L | theorem | Σ¹₂ well-ordering under V=L
s_constructible_reals | state | Constructible reals ℝ∩L
s_infinite_game | state | Infinite game G(A) and strategy
s_determinacy_of_a_set | state | Determinacy of a set Det(A)
s_gale_stewart_theorem | theorem | Gale–Stewart theorem
t_unraveling | technique | Unraveling / covering technique
s_AD_implies_measurable | theorem | AD implies all sets Lebesgue measurable
s_AD_implies_baire_property | theorem | AD implies the Baire property for all sets
s_AD_implies_PSP | theorem | AD implies perfect set property for all sets
t_banach_mazur_game | technique | Banach–Mazur game
s_analytic_determinacy | theorem | Analytic determinacy
s_sharps_analytic_determinacy_equivalence | state | Sharps and analytic determinacy equivalence
t_homogeneous_tree | technique | Homogeneously Suslin set / homogeneous tree
s_martin_steel_pd | theorem | Martin–Steel theorem (projective determinacy)
s_PD_implies_regularity | theorem | PD implies regularity for all projective sets
s_AD_equiconsistent_woodins | theorem | AD equiconsistent with infinitely many Woodins
s_wadge_reducibility | state | Wadge reducibility / Wadge hierarchy
t_solovay_model_construction | technique | Solovay's model construction via Lévy collapse
s_shelah_inaccessible_necessary | theorem | Inaccessible necessary for all sets Lebesgue measurable (Shelah)
