User blog comment:Scorcher007/Analysis DAN up to Z2/@comment-11227630-20180919121102

I don't agree the comparison of S[Ωa+1]. The next admissible ordinal after a is larger than any form of computable function application of a, such as a+1, a×2, a^a, εa+1, Гa+1, etc. and even beyond {1,,...,,1 A 2} (with k-ple comma, A is the separator corresponding with a) for every k. So S[Ωa+1] is much much stronger than you list. It should be at some next "level".