slovodefinícia
von neumann ordinal
(foldoc)		von Neumann ordinal

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)
podobné slovodefinícia
von neumann ordinal
(foldoc)		von Neumann ordinal

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)

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