ZFC axioms

URI: https://gptkb.org/entity/ZFC_axioms

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory gptkb:axiom_system
gptkbp:alternativeTo	gptkb:von_Neumann–Bernays–Gödel_set_theory gptkb:New_Foundations
gptkbp:basisFor	most of modern mathematics
gptkbp:consistsOf	gptkb:Axiom_of_Choice 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_Union gptkb:Axiom_Schema_of_Separation
gptkbp:expressedIn	gptkb:first-order_logic
gptkbp:formedBy	early 20th century
gptkbp:fullName	gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
gptkbp:includes	axiom of choice
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:numberOfAxioms	9 (plus one schema)
gptkbp:standardFormulationOf	gptkb:set_theory
gptkbp:usedIn	foundations of mathematics
gptkbp:bfsParent	gptkb:Axiom_Schema_of_Specification gptkb:axiom_of_Zermelo–Fraenkel_set_theory
gptkbp:bfsLayer	8
http://www.w3.org/2000/01/rdf-schema#label	ZFC axioms