User blog comment:Rgetar/Idea for FGH for larger transfinite ordinals/@comment-35470197-20190702232339/@comment-35470197-20190708094044

> This expression is general form of FGH expressions, where x, αi, βi, k are parameters which may vary for distinct FGH expressions.

It is correct, but this expression is not a general form of a pair of FGH expressions. Using a general form for a single FGH expression is ambiguous. Please read my comment above.

> I think that for distinct lengths there is rule fαβ(x) > x and transitivity.

You are missing the generality, because you are only considering a general expression for a single FGH.