ZFC axioms

URI: https://gptkb.org/entity/ZFC_axioms
GPTKB entity
Statements (28)
Predicate Object
gptkbp:instanceOf gptkb:set_theory
gptkb:axiom_system
gptkbp:alternativeTo gptkb:von_Neumann–Bernays–Gödel_set_theory
gptkb:New_Foundations
gptkbp:basisFor most of modern mathematics
gptkbp:consistsOf 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_Union
gptkb:Axiom_Schema_of_Separation
gptkbp:expressedIn gptkb:first-order_logic
gptkbp:formedBy early 20th century
gptkbp:fullName gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
gptkbp:includes axiom of choice
gptkbp:namedAfter gptkb:Ernst_Zermelo
gptkb:Abraham_Fraenkel
gptkbp:numberOfAxioms 9 (plus one schema)
gptkbp:standardFormulationOf gptkb:set_theory
gptkbp:usedIn foundations of mathematics
gptkbp:bfsParent gptkb:Axiom_Schema_of_Specification
gptkb:axiom_of_Zermelo–Fraenkel_set_theory
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label ZFC axioms