# Existing Set Theory coverage in knowledge_graph.json (Scout output)

ZFC/FOUNDATIONS: s_zfc_axioms, s_axiom_of_choice, s_ac_equivalents, s_tychonoff_equivalent_to_ac, s_axiom_of_extensionality, s_axiom_of_regularity_foundation
ORDINALS: s_ordinal_number, s_limit_ordinal, s_successor_ordinal, s_transfinite_recursion_theorem, t_transfinite_induction, t_transfinite_composition
CARDINALS: s_cardinal_number, s_konig_cardinal_theorem, s_regular_cardinal_arithmetic, s_singular_cardinal_kappa_of_uncountable_cofinality, s_regular_uncountable_cardinal_kappa, s_uncountable_set, s_countable_set, s_erdos_tarski_theorem
LARGE CARDINALS: s_inaccessible_cardinal_axiom, s_measurable_cardinal_axiom, s_woodin_cardinal, s_infinitely_many_woodin_cardinals, s_supercompact_cardinal, s_large_cardinal, s_large_cardinal_consistency_hierarchy, s_real_valued_measurable_cardinal
CONSTRUCTIBLE L: s_constructible_universe_L, s_model_L_of_ZFC_plus_GCH, s_godel_L_model, s_L_hierarchy_L_alpha, s_GCH_in_L, s_con_zfc_gch, s_godels_consistency_of_ch, s_reflection_in_L, s_levy_reflection_in_L, s_phi_reflection_schema_in_L, s_silver_indiscernibles_in_L, s_constructible_closure_L_R
CH/GCH: s_continuum_hypothesis_or_GCH, s_ch_independent_of_zfc, s_model_of_ZFC_plus_not_CH, s_cohens_independence_of_ch
FORCING: s_forcing, s_cohen_forcing, s_forcing_extension_mg, s_generic_extension_V_G, s_generic_extension_with_F, s_generic_filter, s_generic_filter_2, s_generic_random_real, s_random_real_forcing, s_small_forcing_P_below_kappa, s_countable_proper_forcing_class, s_partial_order_for_forcing, t_forcing_technique, t_iterated_forcing, s_complete_BA_for_random_forcing
BOOLEAN-VALUED: s_booleanvalued_model, s_boolean_valued_models, s_boolean_algebra_B, s_boolean_lattice
DIAMOND/COVERING: s_diamond_principle_on_omega_1, s_diamond_implies_suslin_tree, s_diamond_anticipates_antichains, s_jensen_covering
MARTIN'S AXIOM: s_martins_axiom_MA_omega_1, s_MA_implies_SH, s_proper_forcing_axiom, s_PFA_consequences
DETERMINACY: s_axiom_of_determinacy_for_borel_games, s_martin_borel_determinacy, s_martin_analytic_determinacy, s_projective_determinacy, s_determinacy_ad, s_AD_in_L_R
STATIONARY/CLUB: s_stationary_subset_of_kappa, s_diagonal_intersection_club, s_fodor_lemma, s_fodor_constancy_on_stationary_subset, s_solovay_stationary_splitting, s_regressive_function_on_stationary_set
SUSLIN TREES: s_diamond_implies_suslin_tree, s_hypothetical_suslin_tree, s_omega_1_branch_kills_suslin, s_tree_property_for_kappa
RAMSEY/PARTITION: s_ramsey_theorem_finite, s_ramsey_theorem_infinite, s_canonical_ramsey_theorem, s_erdos_rado_theorem, s_partition_relation_kappa_to_kappa_2_2
ULTRAFILTERS: s_ultrafilter, s_existence_of_ultrafilters, s_ultrafilter_limit_in_product, s_ultrafilter_on_index_set, s_ultrapower_embedding_j, s_generic_ultrapower, s_keisler_shelah_theorem
ELEMENTARY EMBEDDINGS: s_elementary_embedding_j_V_to_V
DESCRIPTIVE SET THEORY: s_descriptive_set_theory, s_borel_set, s_borel_algebra, s_borel_sets_in_baire_space, s_borel_subset_of_omega_omega, s_analytic_set_in_baire_space, s_analytic_1_1_set, s_tree_representation_of_analytic_set, s_souslin_theorem, s_lusin_separation_for_disjoint_analytics, s_perfect_set
POLISH: s_polish_space, s_polish_metric_space
REFLECTION/ABSOLUTENESS: s_reflection_principle, s_levy_reflection, s_mostowski_absoluteness, s_shoenfield_absoluteness, s_wellfoundedness_absolute_for_transitive_models
MOSTOWSKI: s_mostowski_collapse, s_mostowski_rank_function
KUNEN: s_kunen_inconsistency, s_kunen_inconsistency_in_L
SILVER/SOLOVAY: s_silver_theorem, s_silver_singular_cardinals_theorem, s_silver_indiscernibles_theorem, s_solovay_model, s_solovay_RVM_theorem, s_levy_solovay_theorem, s_mansfield_solovay
ZORN: s_zorns_lemma, s_maximal_extension_via_zorn, t_zorn_in_topology
SUNFLOWER: s_sunflower_lemma_erdsko, s_sunflower_conjecture, s_sunflower_system
HIERARCHY: s_cumulative_hierarchy_V_alpha, s_wadge_hierarchy_theorem, s_hyperarithmetic_hierarchy
OTHER: s_easton_theorem, s_easton_class_forcing, s_scott_theorem_V_not_L, s_countable_transitive_model, s_countable_elementary_substructure_of_V, s_cantor_bendixson (check), s_cantor_theorem (check), s_cantor_bernstein (check)
