User blog comment:Rgetar/Idea for FGH for larger transfinite ordinals/@comment-35470197-20190702232339/@comment-35470197-20190706235328

Good. I have several comments.

> 4. Define fundamental sequence function α[n] of expression α, n < cof(α).

Is it a function assigning an FGH expression to each FGH expressions (α,n) with n < cof(α)? Namely, is α[n] an FGH expression, which is not the string "α[n]" itself?

If it is correct, then "7. Define a subset of the set of FGH expressions with elements α[n0][n1][n2]...[nk] such as α[n0][n1][n2]...[nk] > α[n0][n1][n2]...[mi] for any mi < ni, i < k." is a little ambiguous. Do you just mean the subset is closed under fundamental sequences? Or are you considering expressions "α[n0][n1][n2]...[nk]" itself? The difference is very important because you do not have a unique way to determine the fundamental sequence expression α[n0][n1][n2]...[nk] from the value of it.

> 5. Prove that α < α[n] and if n > m then α[n] > α[m].

The first inequality is an opposite inequality.