ZF (Zermelo–Fraenkel set theory without choice)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZF
gptkbp:category	gptkb:mathematics gptkb:set_theory
gptkbp:consistencyRelativeTo	ZFC (if ZFC is consistent, so is ZF)
gptkbp:excludesAxiom	gptkb:Axiom_of_Choice
gptkbp:formedBy	early 20th century
gptkbp:fullName	gptkb:Zermelo–Fraenkel_set_theory_without_the_axiom_of_choice
gptkbp:hasAxiom	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:constructible_universe_(L)
gptkbp:hasSubgroup	gptkb:ZFC_(Zermelo–Fraenkel_set_theory_with_Choice)
https://www.w3.org/2000/01/rdf-schema#label	ZF (Zermelo–Fraenkel set theory without choice)
gptkbp:isWeakerThan	gptkb:Zermelo_set_theory gptkb:ZFC_(Zermelo–Fraenkel_set_theory_with_Choice)
gptkbp:mainActivity	gptkb:logic gptkb:set_theory foundations of mathematics
gptkbp:mainLanguage	gptkb:first-order_logic
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:usedIn	foundations of mathematics
gptkbp:bfsParent	gptkb:ZFC_(with_choice)
gptkbp:bfsLayer	6