| 单词 |
von neumann ordinal |
| 释义 |
DictionarySeeordinal numbervon Neumann ordinal
von Neumann ordinal (mathematics)An implementation of ordinals in set theory(e.g. Zermelo Fr?nkel set theory or ZFC). The von Neumannordinal alpha is the well-ordered set containing just theordinals "shorter" than alpha.
"Reasonable" set theories (like ZF) include Mostowski'sCollapsing Theorem: any well-ordered set is isomorphic toa von Neumann ordinal. In really screwy theories (e.g. NFU --New Foundations with Urelemente) this theorem is false.
The finite von Neumann ordinals are the von Neumann integers. |
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