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Meaning of VON NEUMANN ORDINAL

 
Computing Dictionary
 
 Definition: 

An implementation of ordinals in set theory (e.g. zermelo fränkel set theory or zfc). The von Neumann ordinal alpha is the well-ordered set containing just the ordinals "shorter" than alpha.

"Reasonable" set theories (like ZF) include Mostowski's Collapsing Theorem: any well-ordered set is isomorphic to a 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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