von Neumann ordinal
<mathematics> 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.
(1995-03-30)
Nearby terms:
von Neumann integer « von Neumann, John « von
Neumann machine « von Neumann ordinal »
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