Zermelo–Fraenkel set theory with Choice (ZFC)

URI: https://gptkb.org/entity/Zermelo–Fraenkel_set_theory_with_Choice_(ZFC)

GPTKB entity

Statements (51)

Predicate	Object
gptkbp:instanceOf	gptkb:logic gptkb:set_theory
gptkbp:abbreviation	gptkb:ZFC
gptkbp:alternativeTo	gptkb:Kripke–Platek_set_theory gptkb:New_Foundations gptkb:Von_Neumann–Bernays–Gödel_set_theory
gptkbp:basisFor	most of modern mathematics
gptkbp:consistencyUnknown	true
gptkbp:developedBy	gptkb:Ernst_Zermelo gptkb:Thoralf_Skolem gptkb:Abraham_Fraenkel
gptkbp:formedBy	early 20th century
gptkbp:generalizes	gptkb:Zermelo_set_theory
gptkbp:hasAxiom	gptkb:Axiom_of_Choice 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:hasModel	gptkb:von_Neumann_universe
https://www.w3.org/2000/01/rdf-schema#label	Zermelo–Fraenkel set theory with Choice (ZFC)
gptkbp:independenceDate	gptkb:Continuum_Hypothesis gptkb:Axiom_of_Constructibility
gptkbp:language	gptkb:first-order_logic
gptkbp:numberOfAxioms	9
gptkbp:standardFormulationOf	gptkb:set_theory
gptkbp:subjectOf	gptkb:Banach–Tarski_paradox gptkb:Gödel's_incompleteness_theorems gptkb:axiom_of_determinacy gptkb:constructible_universe gptkb:large_cardinal_axioms gptkb:axiom_of_foundation gptkb:well-ordering_theorem gptkb:axiom_of_regularity forcing cardinal numbers ordinal numbers independence proofs inner model theory axiom independence forcing extensions independence of continuum hypothesis set-theoretic paradoxes
gptkbp:usedIn	gptkb:logic gptkb:set_theory foundations of mathematics
gptkbp:bfsParent	gptkb:Axiom_of_Collection
gptkbp:bfsLayer	6