von Neumann universe
(Q77887)
in set theory, the collection of sets obtained by transfinite recursion using the powerset operation
in set theory, the collection of sets obtained by transfinite recursion using the powerset operation
Language:
Current Data About
von Neumann universe
| (P31) |
(Q115489271)
(Q18349448) |
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| (P138) |
(Q17455)
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| (P460) |
(Q2649292)
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| (P2534) |
\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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| (P6104) |
(Q8487137)
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| (P7235) |
V
\beta+1
\mathcal P(-)
\operatorname{Ord}
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other details
| aliases |
cumulative hierarchy von Neumann hierarchy of sets von Neumann hierarchy V |
| description | in set theory, the collection of sets obtained by transfinite recursion using the powerset operation |
External Links
| (P646) |
/m/029dwt
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| (P1417) |
topic/von-Neumann-universe
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