User blog comment:Rgetar/Idea for FGH for larger transfinite ordinals/@comment-35470197-20190702232339/@comment-32213734-20190710115832

Now I think that we need to check 3 things:
 * 1. Recursion in definition of "cof" function terminates.
 * 2. Recursion in definition of "fs" function terminates.
 * 3. fs(...(fs(fs(fs(α, n0), n1), n2)...), nk) terminates.

I tried to prove it for the "new" FGH, and I did not prove it. I proved it only for the "new" FGH without Ω. (I did not prove it for "old" FGH without Ω).

> It is a circular logic.

It is not proved in this step. Such unique string exists only if any sequence α, α[n0], α[n0][n1], α[n0][n1][n2], ... terminates, and it should be checked separately.

I think it is an interesting topic, maybe I will continue to deal with this matter later, but now I have to prepare for the entrance exam in early August. I entered the university last summer, but now I am going to enter another university, which is more consistent with my scientific interests, because I want to become a professional physicist. If I do not enter the university this summer, I will try to enter the university next summer, and so on, because I never surrender at all.