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...

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...

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

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...

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...

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

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

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...

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

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

given by the natural operations. It has also been shown (in von Neumann–Bernays–Gödel set theory) that the maximal class hyperreal field is isomorphic to...

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,...

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...

Kurt Gödel's 1938 proof of the relative consistency of the axiom of choice and the generalized continuum hypothesis to 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...

John von Neumann (/vɒn ˈnɔɪmən/ von NOY-mən; Hungarian: Neumann János Lajos [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian...

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

ordinal numbers. Such set theories include Von Neumann–Bernays–Gödel set theory, and Morse–Kelley set theory. In such set theories, it is perfectly fine...

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...

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...

theory for mathematics. Other formalizations of set theory have been proposed, including von Neumann–Bernays–Gödel set theory (NBG), Morse–Kelley set...

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...

strictly stronger than it. In class theories such as Von Neumann–Bernays–Gödel set theory and Morse–Kelley set theory, there is an axiom called the axiom...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

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...

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

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...

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...