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axiom of ZFC
URI:
https://gptkb.org/entity/axiom_of_ZFC
GPTKB entity
Statements (28)
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
https://www.w3.org/2000/01/rdf-schema#label
axiom of ZFC
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