von Neumann–Bernays–Gödel axioms

URI: https://gptkb.org/entity/von_Neumann–Bernays–Gödel_axioms
GPTKB entity
Statements (34)
Predicate Object
gptkbp:instanceOf gptkb:set_theory
gptkbp:allows proper classes
gptkbp:alsoKnownAs gptkb:NBG_axioms
gptkbp:equiconsistentWith gptkb:Zermelo–Fraenkel_set_theory
gptkbp:feature distinguishes between sets and classes
gptkbp:field gptkb:logic
gptkb:set_theory
gptkbp:formedBy 1920s
gptkbp:generalizes gptkb:Zermelo–Fraenkel_set_theory
gptkbp:hasAxiom Infinity
Union
Choice
Regularity
Replacement
Class Comprehension
Extensionality
Pairing
Power Set
Set Existence
gptkbp:hasModel gptkb:von_Neumann_universe
https://www.w3.org/2000/01/rdf-schema#label von Neumann–Bernays–Gödel axioms
gptkbp:influenced gptkb:Morse–Kelley_set_theory
gptkbp:influencedBy gptkb:Zermelo–Fraenkel_axioms
gptkbp:namedAfter gptkb:John_von_Neumann
gptkb:Kurt_Gödel
gptkb:Paul_Bernays
gptkbp:publishedBy gptkb:John_von_Neumann
gptkb:Kurt_Gödel
gptkb:Paul_Bernays
gptkbp:type first-order theory
gptkbp:usedFor formalizing mathematics involving classes
gptkbp:usedIn foundations of mathematics
gptkbp:bfsParent gptkb:Set_theory
gptkbp:bfsLayer 5