Unstratified mathematical induction enables proving that there are " n "-Mahlo cardinals for every " n ", given " Cantorian Sets ", which gives an extension of ZFC that is even stronger than the previous one, which only asserts that there are " n "-Mahlos for each concrete natural number ( leaving open the possibility of nonstandard counterexamples ).
22.
In NFU, it is not obvious that this approach can be used, since the successor operation y \ cup \ { y \ } is unstratified and so the set " N " as defined above cannot be shown to exist in NFU ( it is interesting to note that it is consistent for the set of finite von Neumann ordinals to exist in NFU, but this strengthens the theory, as the existence of this set implies the Axiom of Counting ( for which see below or the New Foundations article ) ).
