Zermelo–Fraenkel set theory without the Axiom of Choice

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZF
gptkbp:developedBy	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:excludesAxiom	gptkb:Axiom_of_Choice
gptkbp:generalizes	gptkb:Zermelo_set_theory
gptkbp:hasAxiom	gptkb:Axiom_of_Empty_Set 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
https://www.w3.org/2000/01/rdf-schema#label	Zermelo–Fraenkel set theory without the Axiom of Choice
gptkbp:introducedIn	1922
gptkbp:isConsistentIf	ZF is consistent if ZFC is consistent
gptkbp:isFoundationFor	most of modern mathematics
gptkbp:isSubtheoryOf	gptkb:Zermelo–Fraenkel_set_theory_with_the_Axiom_of_Choice
gptkbp:partOf	gptkb:logic foundations of mathematics
gptkbp:symbol	gptkb:ZF
gptkbp:usedIn	gptkb:logic gptkb:set_theory model theory
gptkbp:bfsParent	gptkb:ZF_(Zermelo–Fraenkel_set_theory_without_Choice)
gptkbp:bfsLayer	7