User blog comment:Wythagoras/FGH of Dollar Function new version/@comment-11227630-20131109131352/@comment-10429372-20131110064244

Oh, that ordinal notation? I recently discovered that it isn't very strong.

α->Ξα(0) = lim(Ω, ΞΩ(0), ΞΞ Ω(0) (0), ΞΞΞ Ω(0) (0) (0), ΞΞΞ Ξ Ω(0) (0) (0) (0), ...)

Yes, after that we can have an super-diagonalizer, U:

ΞU(0) = α->Ξα(0). After that we can have ΞU+1(0), ΞU2(0), Ξe U+1 (0), ΞΩ U+1 (0), ΞU 2 (0), ... and we can have an inaccessible-ultimate, compact-ultimate, ultimate-ultimate, omega-ex-ultimate, ...

Then we reach the second-ultimate ordinal, ΞU(2)(0). Then we make an ordinal diagonalizing over the brackets inside U...

This is still weaker than the ordinal describing Loaders function.