User blog comment:Syst3ms/A formal definition for UNOCF/@comment-35470197-20180728080043/@comment-35470197-20180728151950

> What you have to understand is that cardinals in UNOCF have nothing to do with set theory.

I know that the symbols are just constant term symbols. But to show the well-definedness of OCFs with such symbols, one usually uses set theory. It is ok if you have a full formal proof of the wll-definedness, but you do not seem to have.

No non-trivial statements are provable if you do not assume axioms. If you think that you do not use large cardinals, you need other axioms, e.g. \(\textrm{ZFC}\), \(\textrm{PA}\), or \(\textrm{PRA}\).

Evemn if the behaviour does not change, the provability of the termination can change. If the termination is not provable, there is a model in which the termination is actutally false by the incompleteness theorem.

If you think that declaring axioms are irrelevant, then you do not know the definition of the notion of a formal proof, right...?

> On an unrelated note, I'd suggest joining the googology discord server, that way discussing can be made much easier ^^

Oh, you think that my questions are unrelated...? I think that such arguments are strongly necessary for application to a formal proof. But if you think so, I stop asking. Sorry.