Von Neumann–Bernays–Gödel Set Theory

URI: https://gptkb.org/entity/Von_Neumann–Bernays–Gödel_Set_Theory

GPTKB entity

Statements (51)

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:NBG
gptkbp:allows	proper classes
gptkbp:alternativeTo	gptkb:Morse–Kelley_set_theory
gptkbp:basedOn	gptkb:Zermelo–Fraenkel_set_theory
gptkbp:conservativeExtensionOf	gptkb:Zermelo–Fraenkel_set_theory
gptkbp:developedBy	gptkb:John_von_Neumann gptkb:Kurt_Gödel gptkb:Paul_Bernays
gptkbp:distinctiveFeature	classes sets
gptkbp:equivalentTo	Zermelo–Fraenkel set theory (for sets)
gptkbp:firstPublished	1920s
gptkbp:formalizes	set-class distinction
gptkbp:hasAxiom	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_of_Class_Comprehension gptkb:Axiom_of_Foundation finite set of axioms Axiom of Class Choice Axiom of Class Elementhood Axiom of Class Existence Axiom of Class Extensionality Axiom of Class Foundation Axiom of Class Infinity Axiom of Class Pairing Axiom of Class Power Set Axiom of Class Regularity Axiom of Class Replacement Axiom of Class Specification Axiom of Class Subset Axiom of Class Union Axiom of Elementhood Axiom of Subset
https://www.w3.org/2000/01/rdf-schema#label	Von Neumann–Bernays–Gödel Set Theory
gptkbp:namedAfter	gptkb:John_von_Neumann gptkb:Kurt_Gödel gptkb:Paul_Bernays
gptkbp:usedFor	gptkb:category_theory model theory
gptkbp:usedIn	gptkb:logic foundations of mathematics
gptkbp:bfsParent	gptkb:Axiomatic_Set_Theory
gptkbp:bfsLayer	7