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gptkbp:instanceOf
|
gptkb:set_theory
|
|
gptkbp:abbreviation
|
gptkb:NBG
|
|
gptkbp:allows
|
proper classes
|
|
gptkbp:compatibleWith
|
classes as elements of other classes
|
|
gptkbp:distinctiveFeature
|
proper classes
sets
|
|
gptkbp:equivalentTo
|
gptkb:ZFC_for_sets
|
|
gptkbp:formedBy
|
1920s
|
|
gptkbp:fullName
|
gptkb:von_Neumann–Bernays–Gödel_set_theory
|
|
gptkbp:hasAxiom
|
gptkb:set_theory
gptkb:Axiom_of_Choice
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
|
|
gptkbp:hasFeature
|
class comprehension is restricted
every set is a class
not every class is a set
proper classes cannot be members of classes
|
|
gptkbp:heldBy
|
consistent if ZFC is consistent
finitely axiomatizable
first-order theory
standard set theory with classes
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
NBG set theory
|
|
gptkbp:includes
|
classes
sets
|
|
gptkbp:isConservativeExtensionOf
|
gptkb:Zermelo–Fraenkel_set_theory
|
|
gptkbp:isMoreConciseThan
|
gptkb:ZFC
|
|
gptkbp:namedAfter
|
gptkb:John_von_Neumann
gptkb:Kurt_Gödel
gptkb:Paul_Bernays
|
|
gptkbp:publishedIn
|
gptkb:Kurt_Gödel's_1940_monograph
gptkb:John_von_Neumann's_1925_and_1929_papers
Paul Bernays' 1937-1954 works
|
|
gptkbp:relatedTo
|
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Morse–Kelley_set_theory
gptkb:von_Neumann_universe
|
|
gptkbp:usedBy
|
set theorists
logicians
mathematical foundations researchers
|
|
gptkbp:usedFor
|
gptkb:category_theory
model theory
metamathematics
formalizing mathematics
studying large cardinals
|
|
gptkbp:usedIn
|
foundations of mathematics
|
|
gptkbp:bfsParent
|
gptkb:NBG
gptkb:MK_set_theory
|
|
gptkbp:bfsLayer
|
6
|