Zermelo–Fraenkel axioms

URI: https://gptkb.org/entity/Zermelo–Fraenkel_axioms

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:axiomatic_system
gptkbp:abbreviation	gptkb:ZF gptkb:ZFC_(with_axiom_of_choice)
gptkbp:alsoKnownAs	ZF axioms
gptkbp:category	gptkb:logic gptkb:set_theory
gptkbp:consistsOf	gptkb:axiom_schema_of_replacement gptkb:axiom_of_empty_set gptkb:axiom_of_extensionality gptkb:axiom_of_pairing gptkb:axiom_of_power_set gptkb:axiom_of_regularity gptkb:axiom_of_union gptkb:axiom_schema_of_separation axiom of infinity
gptkbp:extendsTo	gptkb:Zermelo–Fraenkel_set_theory_with_choice
gptkbp:field	gptkb:set_theory
gptkbp:formedBy	early 20th century
gptkbp:influencedBy	gptkb:Russell's_paradox
gptkbp:language	gptkb:first-order_logic
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:purpose	avoid set-theoretic paradoxes
gptkbp:relatedTo	gptkb:Peano_axioms gptkb:Von_Neumann–Bernays–Gödel_set_theory axiom of choice
gptkbp:replacedBy	gptkb:naive_set_theory
gptkbp:usedIn	foundations of mathematics
gptkbp:bfsParent	gptkb:Set_Theory
gptkbp:bfsLayer	5
https://www.w3.org/2000/01/rdf-schema#label	Zermelo–Fraenkel axioms