User blog comment:Hyp cos/Analysis - BEAF, FGH and SGH (part 3)/@comment-1605058-20131029153716/@comment-1605058-20131030161726

I don't really get what "active point" is. ω nests isn't also good term, as we can't have transfinitely many nests on such function, as it can become ambiguous. For example, ω^ω^ω^... (with ω nests) can be any epsilon number - we said nothing about what is "on top" of this stack.

Saying "it works for C(α+1), C(α+ω), C(α2), C(αω)" isn't suffiscient reason for me. On a similar reasoning (by comparing to Bird's notation, as it works up to Feferman-Schutte ordinal), Ikosarakt once said that SGH and FGH meet at LVO, and it turned out to not be right.