User blog comment:Rgetar/Idea for FGH for larger transfinite ordinals/@comment-35470197-20190702232339/@comment-32213734-20190708075056

> Do you mean "well-founded partial ordered set" instead of "well-founded set"?

I read about well-founded sets and I found out that actually I meant set with well-founded relation, not well-founded set, since I read that "well-founded set" is about axiom of regularity, not about minimal elements. And actually I meant total order, since I thought that any two elements should be comparable, that is well-order. So, "well-founded" in my comment should be replaced with "well-ordered".

> single expression

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

> What you need to define is the comparison between two expressions which are possibly of distinct lengths.

I think that for distinct lengths there is rule fαβ(x) > x and transitivity. Or, it can be stated that if during comparison we reached the left edge of one and only one of two compared FGH expressions, then the expression, which ended, is lesser.

> What is the relation between i and k?

I formulated this definition not quite correct, since "i" in αi, βi and in Si, Si + 1 are actually two different variables. In this definition I again meant the "general form" of FGH expressions


 * fα k βk(...(fα 2 β2(fα 1 β1(x)))...)

where x, αi, βi, k are parameters. So, I meant that Sj + 1 is set of all fα k βk(...(fα 2 β2(fα 1 β1(x)))...) such as x, αi, βi ∈ Sj; k ∈ ℕ; α1 > α2 > ... > αk.