S> 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 iSiSomorphic 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)
