Zermelo–Fraenkel set theory with the Axiom of Choice

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZFC
gptkbp:field	gptkb:logic gptkb:set_theory
gptkbp:formedBy	early 20th century
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
https://www.w3.org/2000/01/rdf-schema#label	Zermelo–Fraenkel set theory with the Axiom of Choice
gptkbp:isConsistentWith	gptkb:Axiom_of_Choice
gptkbp:isFoundationFor	modern mathematics most of classical mathematics
gptkbp:isStandardFormulationOf	gptkb:set_theory
gptkbp:isWeakerThan	gptkb:Zermelo–Fraenkel_set_theory gptkb:Zermelo–Fraenkel_set_theory_with_large_cardinal_axioms
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:relatedTo	gptkb:Gödel's_incompleteness_theorems gptkb:Russell's_paradox gptkb:von_Neumann–Bernays–Gödel_set_theory gptkb:Peano_arithmetic gptkb:Continuum_Hypothesis gptkb:New_Foundations gptkb:axiom_of_determinacy gptkb:constructible_universe gptkb:large_cardinal_axioms gptkb:axiom_of_foundation forcing axiom schema axiom independence axiom of choice controversy
gptkbp:usedIn	gptkb:algebra gptkb:logic gptkb:topology gptkb:category_theory analysis computer science model theory number theory proof theory combinatorics mathematical foundations
gptkbp:bfsParent	gptkb:ZFC_(with_Axiom_of_Choice)
gptkbp:bfsLayer	6