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:logic gptkb:topology gptkb:category_theory gptkb:cardinal_arithmetic gptkb:constructible_universe gptkb:set-theoretic_topology gptkb:descriptive_set_theory abstract algebra functional analysis measure theory model theory number theory proof theory recursion theory theoretical computer science combinatorics 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)
https://www.w3.org/2000/01/rdf-schema#label	Zermelo-Fraenkel set theory with Choice (ZFC)
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