Von Neumann–Bernays–Gödel set theory

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:NBG
gptkbp:allows	quantification over classes quantification over sets
gptkbp:alternativeTo	gptkb:Zermelo–Fraenkel_set_theory gptkb:Morse–Kelley_set_theory
gptkbp:conservativeOver	gptkb:Zermelo–Fraenkel_set_theory
gptkbp:developedBy	gptkb:John_von_Neumann gptkb:Kurt_Gödel gptkb:Paul_Bernays
gptkbp:distinción	gptkb:box_set proper class
gptkbp:firstPublished	1920s
gptkbp:hasAxiom	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:hasProperty	every set is a class not every class is a set avoids Russell's paradox axiomatizes classes and sets proper classes cannot be members of other classes
https://www.w3.org/2000/01/rdf-schema#label	Von Neumann–Bernays–Gödel set theory
gptkbp:includes	classes sets
gptkbp:influenced	gptkb:Morse–Kelley_set_theory gptkb:category_theory
gptkbp:influencedBy	gptkb:Zermelo–Fraenkel_set_theory
gptkbp:language	gptkb:first-order_logic
gptkbp:namedAfter	gptkb:John_von_Neumann gptkb:Kurt_Gödel gptkb:Paul_Bernays
gptkbp:publishedIn	gptkb:Mathematische_Annalen
gptkbp:subjectOf	gptkb:logic gptkb:set_theory foundations of mathematics
gptkbp:type	conservative extension of Zermelo–Fraenkel set theory
gptkbp:usedIn	gptkb:logic foundations of mathematics
gptkbp:bfsParent	gptkb:set_theory
gptkbp:bfsLayer	4