User blog comment:P進大好きbot/New Googological Ruler/@comment-31580368-20190629142620/@comment-31580368-20190630073323

"I am 95% certain that you do not understand the definition of PTO".

Speaking of PTO, we can only talk about constructed models and structures below this, that can be proved by this theory. Stronger theories allow me to think about richer structures, such as Large countable ordinals, which I can use for example in OCF.

I say that it is connected more with philosophy. If you do not believe in the existence of structures that you cannot build, then you are not a Platonist. This is a constructive approach, I have nothing against it. From this point of view, functions such as FOOT will actually be ill-defined.