Zermelo-Fraenkel set theory with Choice (ZFC)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZFC
gptkbp:axiomatizes	sets
gptkbp:basisFor	gptkb:combinatorics gptkb:theoretical_computer_science gptkb:logic gptkb:topology gptkb:model_theory gptkb:category_theory gptkb:cardinal_arithmetic gptkb:constructible_universe gptkb:set-theoretic_topology gptkb:descriptive_set_theory abstract algebra functional analysis measure theory number theory proof theory recursion theory forcing real analysis ordinal arithmetic inner model theory large cardinal theory
gptkbp:consistencyUndecidable	true (by Gödel's incompleteness theorems)
gptkbp:developedBy	gptkb:Ernst_Zermelo gptkb:Thoralf_Skolem gptkb:Abraham_Fraenkel
gptkbp:excludes	proper classes
gptkbp:formedBy	early 20th century
gptkbp:generalizes	gptkb:Zermelo_set_theory
gptkbp:hasAxiom	gptkb:Axiom_of_Choice gptkb:Axiom_of_Extensionality gptkb:Axiom_of_Infinity gptkb:Axiom_of_Pairing gptkb:Axiom_of_Power_Set gptkb:Axiom_of_Regularity gptkb:Axiom_of_Replacement gptkb:Axiom_of_Separation gptkb:Axiom_of_Union
gptkbp:hasSubgroup	class theories (e.g., NBG, MK)
gptkbp:independentStatement	gptkb:Continuum_Hypothesis gptkb:Axiom_of_Constructibility_(V=L)
gptkbp:language	gptkb:first-order_logic
gptkbp:standardFoundationFor	most of modern mathematics
gptkbp:usedIn	gptkb:logic gptkb:set_theory foundations of mathematics
gptkbp:bfsParent	gptkb:Zermelo-Fraenkel_set_theory_(ZF)
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	Zermelo-Fraenkel set theory with Choice (ZFC)