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 (104)

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZFC
gptkbp:basisFor	most of mathematics
gptkbp:consistencyRelativeTo	gptkb:Zermelo-Fraenkel_set_theory_(ZF)
gptkbp:field	gptkb:logic gptkb:set_theory
gptkbp:formedBy	early 20th century
gptkbp:hasAxiom	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
gptkbp:isConsistentIf	no contradiction can be derived from its axioms
gptkbp:isCountablyAxiomatizable	true
gptkbp:isFirstOrderTheory	true
gptkbp:isFoundationFor	gptkb:combinatorics gptkb:algebraic_geometry gptkb:logic gptkb:probability_theory gptkb:model_theory gptkb:Banach_spaces gptkb:Hilbert_spaces gptkb:set-theoretic_topology gptkb:descriptive_set_theory complex analysis computability theory functional analysis measure theory number theory proof theory recursion theory fields trees groups mathematical objects graph theory homotopy theory algebraic varieties categories graphs homological algebra ideals modules real analysis real numbers sequences vector spaces filters differentiable manifolds rings topological spaces natural numbers functions lattices partially ordered sets relations ultrafilters cohomology theories metric spaces schemes cardinals higher category theory smooth manifolds functors model categories natural transformations manifolds measure spaces probability spaces sigma-algebras Boolean algebras compact spaces locally compact spaces topoi sheaves connected spaces discrete spaces measurable spaces ordinals presheaves well-ordered sets
gptkbp:isIncomplete	true
gptkbp:isUndecidable	true
gptkbp:isWeakerThan	gptkb:Kelley–Morse_set_theory gptkb:Zermelo-Fraenkel_set_theory_(ZF) Von Neumann–Bernays–Gödel set theory (NBG)
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:standardFoundationFor	modern mathematics
gptkbp:usedIn	gptkb:analysis gptkb:algebra gptkb:topology gptkb:model_theory gptkb:category_theory number theory
gptkbp:bfsParent	gptkb:Continuum_Hypothesis gptkb:Generalized_Continuum_Hypothesis
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC)