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.

单词	von neumann ordinal
释义	DictionarySeeordinal number von 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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