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mathematics
An implementation of
ordinals
in
set theory
(e.g.
Zermelo Frankel 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 Neumannintegers
.
(1995-03-30)