mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC)...

set containing all sets) nor for unrestricted comprehension, thereby avoiding Russell's paradox. Von Neumann–Bernays–Gödel set theory (NBG) is a commonly...

Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the...

In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary...

Zermelo–Fraenkel set theory (ZF) and its extensions, such as von Neumann–Bernays–Gödel set theory (NBG). It bears certain differences from its descendants...

replacement. Sets and proper classes. These include Von Neumann–Bernays–Gödel set theory, which has the same strength as ZFC for theorems about sets alone,...

first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory restricts the...

because it is not itself a set. Universe (mathematics) Grothendieck universe Domain of discourse Von Neumann–Bernays–Gödel set theory — an extension of ZFC...

Kripke–Platek set theory with urelements and the variant of Von Neumann–Bernays–Gödel set theory described by Mendelson. In type theory, an object of...

handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from...

Kurt Gödel's proof of the relative consistency of the axiom of choice and the generalized continuum hypothesis to Von Neumann–Bernays–Gödel set theory. (The...

primitive. Bernays recast von Neumann's theory so that classes and sets were primitive. Bernays's theory, with modifications by Kurt Gödel, is known as von Neumann–Bernays–Gödel...

theorem von Neumann stability analysis von Neumann universal constructor von Neumann universe von Neumann–Bernays–Gödel set theory von Neumann–Morgenstern...

division); as such, they form an ordered field. If formulated in von Neumann–Bernays–Gödel set theory, the surreal numbers are a universal ordered field in the...

a subset of any set X, and is therefore not a set in ZFC. In some extensions of ZFC, notably in von Neumann–Bernays–Gödel set theory, objects like R are...

set theory by the axioms of Zermelo–Fraenkel set theory. Alternative set theories include: Vopěnka's alternative set theory Von Neumann–Bernays–Gödel...

sets. In its use of classes, AST differs from other alternative set theories such as Morse–Kelley set theory and Von Neumann–Bernays–Gödel set theory...

Von Neumann–Bernays–Gödel set theory (NBG) and Morse–Kelley set theory. Later expositions of class theories—such as those of Paul Bernays, Kurt Gödel...

complement in positive set theory. In von Neumann–Bernays–Gödel set theory, a distinction is made between sets and classes. A class C is a set if and only if...

set theory Tarski–Grothendieck set theory Von Neumann–Bernays–Gödel set theory Zermelo–Fraenkel set theory Zermelo set theory Set (mathematics) Set-builder...

Petr Hájek (1972). It is based on a modification of the von Neumann–Bernays–Gödel set theory; in standard NBG, the existence of semisets is precluded by...

set theory; and D e f ( V κ ) {\displaystyle Def(V_{\kappa })} is one of the intended models of Mendelson's version of Von Neumann–Bernays–Gödel set theory...

of ZFC are also theorems of von Neumann–Bernays–Gödel set theory, but the latter can be finitely axiomatized. The set theory New Foundations can be finitely...

Kurt Gödel. It's Not All In The Numbers: Gregory Chaitin Explains Gödel's Mathematical Complexities. Gödel photo gallery. (archived) Kurt Gödel MacTutor...

theorem, von Neumann obtained a proof of the second incompleteness theorem, which he announced to Gödel in a letter dated November 20, 1930. Gödel had independently...

years". Rubin's dissertation was entitled Free Algebras in Von Neumann–Bernays–Gödel Set Theory and Positive Elementary Inductions in Reasonable Structures...

Zermelo–Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann–Bernays–Gödel set theory, a conservative...

representative set to each equivalence class (cardinal assignment). In some other systems of axiomatic set theory, for example in Von Neumann–Bernays–Gödel set theory...

arithmetic). Von Neumann–Bernays–Gödel set theory ( N B G {\displaystyle {\mathsf {NBG}}} ) is a conservative extension of Zermelo–Fraenkel set theory with the...

appendix sets out a new approach to axiomatic set theory, now called Morse–Kelley set theory, that builds on Von Neumann–Bernays–Gödel set theory. He introduced...