Zermelo-Fraenkel Set Theory

URI: https://gptkb.org/entity/Zermelo-Fraenkel_Set_Theory

GPTKB entity

Statements (51)

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZF gptkb:ZFC
gptkbp:category	gptkb:logic gptkb:mathematics gptkb:set_theory
gptkbp:consistencyUndecidable	gptkb:Gödel's_incompleteness_theorems
gptkbp:formedBy	early 20th century
gptkbp:hasAxiom	gptkb:Axiom_of_extensionality gptkb:Axiom_of_infinity gptkb:Axiom_of_pairing gptkb:Axiom_of_power_set gptkb:Axiom_of_regularity gptkb:Axiom_of_union gptkb:Axiom_of_empty_set gptkb:Axiom_of_foundation
gptkbp:hasAxiomSchema	gptkb:Axiom_schema_of_replacement gptkb:Axiom_schema_of_separation
gptkbp:hasModel	gptkb:von_Neumann_universe
https://www.w3.org/2000/01/rdf-schema#label	Zermelo-Fraenkel Set Theory
gptkbp:influencedBy	gptkb:Ernst_Zermelo gptkb:Thoralf_Skolem gptkb:Abraham_Fraenkel
gptkbp:language	gptkb:first-order_logic
gptkbp:mainAxiom	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:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:prevention	gptkb:Russell's_paradox
gptkbp:relatedTo	gptkb:Morse–Kelley_set_theory gptkb:Peano_axioms gptkb:Tarski–Grothendieck_set_theory gptkb:New_Foundations Gödel–Bernays set theory
gptkbp:replacedBy	gptkb:naive_set_theory
gptkbp:standardFormulationOf	gptkb:set_theory
gptkbp:usedIn	gptkb:logic gptkb:set_theory foundations of mathematics
gptkbp:withAxiomOfChoice	gptkb:ZFC
gptkbp:withoutAxiomOfChoice	gptkb:ZF
gptkbp:bfsParent	gptkb:Axiomatic_Set_Theory
gptkbp:bfsLayer	7