User blog comment:Rgetar/Idea for FGH for larger transfinite ordinals/@comment-35470197-20190702232339/@comment-35470197-20190707085832

> Let S0 is well-founded set.

What do you mean? "Let S_0 be an arbitary well-founded set" or something like that? If you use S_0 in the definition of the notion of an FGH-expression, you need to define it. Moreover, every set is well-founded in ZFC set theory. Do you mean "well-founded partial ordered set" instead of "well-founded set"?

> Comparison

The definiton is informal, because you just declare a single expression. What you need to define is the comparison between two expressions which are possibly of distinct lengths.

> Let S_{i + 1} is set of all FGH expressions such as

What is the relation between i and k? Do you mean "S_{i + 1} is set of all FGH expressions satisfying k ≧ i such as ..."?