axiom of ZFC

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

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:abbreviation	Zermelo-Fraenkel set theory with the Axiom of Choice
gptkbp:alternativeTo	gptkb:von_Neumann–Bernays–Gödel_set_theory gptkb:Kripke–Platek_set_theory gptkb:New_Foundations
gptkbp:basisFor	modern mathematics
gptkbp:consistencyUndecidable	true
gptkbp:expressedIn	gptkb:first-order_logic
gptkbp:formedBy	early 20th century
gptkbp:includes	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_Separation gptkb:Axiom_of_Union
gptkbp:independenceDate	gptkb:Continuum_Hypothesis
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:numberOfAxioms	9
gptkbp:partOf	gptkb:Zermelo-Fraenkel_set_theory
gptkbp:usedIn	gptkb:set_theory
gptkbp:bfsParent	gptkb:axiom_schema_of_replacement
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	axiom of ZFC