In article <email@example.com>, David Bernier <firstname.lastname@example.org> wrote:
> Obviously, one wants ordinals of uncountable order type. > In ZC without any additional axioms, it would seem that one > can only prove the existence of von Neumann ordinals that are > countable (either finite or infinite). > > So in plain ZC, what would be a good definition of an > ordinal?
Is there any reason why one cannot use the same definition as in ZF and NBG?
The von Neumann definition of NBG is : A set S is an ordinal if and only if S is totally ordered with respect to set containment and every element of S is also a subset of S.