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:alternativeTo	gptkb:Kelley–Morse_set_theory gptkb:New_Foundations gptkb:Von_Neumann–Bernays–Gödel_set_theory gptkb:Zermelo–Fraenkel_set_theory_(ZF)
gptkbp:axiomOfChoiceStatus	included
gptkbp:consistencyUndecidable	gptkb:Gödel's_incompleteness_theorems
gptkbp:field	gptkb:logic gptkb:set_theory
gptkbp:formedBy	early 20th century
gptkbp:generalizes	gptkb:Zermelo_set_theory
gptkbp:hasAxiom	gptkb:set_theory 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:hasModel	gptkb:von_Neumann_universe
https://www.w3.org/2000/01/rdf-schema#label	Zermelo–Fraenkel set theory with the axiom of choice (ZFC)
gptkbp:isConsistentIf	ZFC is consistent if ZF is consistent
gptkbp:isCumulativeHierarchy	true
gptkbp:isFirstOrderTheory	true
gptkbp:isFoundationFor	gptkb:logic gptkb:topology gptkb:category_theory gptkb:set-theoretic_topology abstract algebra functional analysis group theory measure theory model theory number theory combinatorics cardinal numbers mathematical foundations ordinal numbers real analysis
gptkbp:isWellFounded	true
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:standardFoundationFor	modern mathematics
gptkbp:usedFor	foundation of mathematics
gptkbp:bfsParent	gptkb:Continuum_hypothesis
gptkbp:bfsLayer	5