(Q77887)

English

von Neumann universe

in set theory, the collection of sets obtained by transfinite recursion using the powerset operation

cumulative hierarchy
von Neumann hierarchy of sets
von Neumann hierarchy
V

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{\begin{aligned}V_{\alpha }&={\begin{cases}{\mathcal {P}}(V_{\beta })&\exists \beta \colon \alpha =\beta +1\\\bigcup _{\gamma <\alpha }V_{\gamma }&\nexists \beta \colon \alpha =\beta +1\end{cases}}\\V&=\bigcup _{\alpha \in \operatorname {Ord} }V_{\alpha }\end{aligned}}

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in defining formula

V

symbol represents

von Neumann universe

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\beta +1

symbol represents

successor ordinal

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{\mathcal {P}}(-)

symbol represents

power set

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\operatorname {Ord}

symbol represents

ordinal number

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maintained by WikiProject

WikiProject Mathematics

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said to be the same as

universal class

statement supported by

axiom of regularity

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Encyclopædia Britannica Online ID

topic/von-Neumann-universe

subject named as

von Neumann universe

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28 October 2013

(Q77887)

von Neumann universe

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