Zermelo-Fraenkel set theory with the axiom of choice (ZFC)

URI: https://gptkb.org/entity/Zermelo-Fraenkel_set_theory_with_the_axiom_of_choice_(ZFC)

GPTKB entity

Statements (50)

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZFC
gptkbp:consistencyRelativeTo	gptkb:Zermelo-Fraenkel_set_theory_(ZF)
gptkbp:field	gptkb:logic gptkb:set_theory
gptkbp:formedBy	early 20th century
gptkbp:generalizes	gptkb:Zermelo_set_theory
gptkbp:hasAxiom	gptkb:mathematics gptkb:set_theory 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 gptkb:Axiom_of_Foundation
gptkbp:hasModel	gptkb:von_Neumann_universe
gptkbp:hasUndecidableStatements	gptkb:Continuum_Hypothesis gptkb:Axiom_of_Constructibility
https://www.w3.org/2000/01/rdf-schema#label	Zermelo-Fraenkel set theory with the axiom of choice (ZFC)
gptkbp:isConsistentIf	no contradiction can be derived from its axioms
gptkbp:isCountablyAxiomatizable	true
gptkbp:isFirstOrderTheory	true
gptkbp:isFoundationFor	most of mathematics
gptkbp:isIncomplete	true
gptkbp:isWeakerThan	gptkb:Zermelo-Fraenkel_set_theory_(ZF)
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:relatedTo	gptkb:Gödel's_incompleteness_theorems gptkb:axiom_of_determinacy gptkb:constructible_universe gptkb:large_cardinal_axioms forcing
gptkbp:standardFoundationFor	modern mathematics
gptkbp:usedBy	gptkb:mathematician logicians philosophers of mathematics
gptkbp:usedIn	gptkb:algebra gptkb:logic gptkb:topology gptkb:category_theory analysis model theory number theory combinatorics
gptkbp:bfsParent	gptkb:continuum_hypothesis
gptkbp:bfsLayer	5