Cs> An implementation of ordinals in set theory (e.g. Zermelo Fränkel set theory or ZFC). The von Neumann ordinal alpha is the well-ordered setContaining 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)
