Zermelo–Fraenkel set theory with the axiom of choice

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZFC
gptkbp:basisFor	gptkb:cardinal_arithmetic ordinal arithmetic most of classical mathematics
gptkbp:field	gptkb:mathematics
gptkbp:formedBy	early 20th century
gptkbp:generalizes	gptkb:naive_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_Union gptkb:Axiom_Schema_of_Replacement gptkb:Axiom_Schema_of_Separation
gptkbp:hasModel	gptkb:von_Neumann_universe
https://www.w3.org/2000/01/rdf-schema#label	Zermelo–Fraenkel set theory with the axiom of choice
gptkbp:isConsistentWith	gptkb:first-order_logic
gptkbp:isFoundationFor	modern mathematics
gptkbp:isWeakerThan	gptkb:Zermelo–Fraenkel_set_theory gptkb:Morse–Kelley_set_theory
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:relatedTo	gptkb:Gödel's_incompleteness_theorems gptkb:Continuum_Hypothesis gptkb:axiom_of_determinacy gptkb:constructible_universe gptkb:large_cardinal_axioms gptkb:axiom_of_foundation gptkb:axiom_of_extensionality gptkb:axiom_of_pairing gptkb:axiom_of_power_set gptkb:axiom_of_union gptkb:axiom_of_separation forcing independence proofs axiom of infinity axiom of replacement
gptkbp:usedFor	foundation of mathematics
gptkbp:bfsParent	gptkb:ZFC gptkb:ZFC_(with_choice)
gptkbp:bfsLayer	6