User blog comment:SuperSpruce/Question about certain fundamental sequences/@comment-32213734-20190422053122/@comment-32213734-20190424164535

I read article about Buchholz's function and tried to study it. Now I'm not sure that in previous comment I correctly matched ψ function with my notation, but I think that I correctly wrote fundamental sequence of ψ((Ω_ω)+Ω_2), since #452 in Scorcher007's list is ψ(Ωω+ψ1(Ωω+ψ1(Ωω+ψ1(Ωω+ψ1(...))))) = ψ(Ωω+Ω2).

As I understand, ψ(...) is finite or countable ordinal, that is ψ(...) < Ω; ψ1(...) is ordinal of cardinality Ω, that is Ω ≤ ψ1(...) < Ω2; ψ2(...) is ordinal of cardinality Ω2, that is Ω2 ≤ ψ1(...) < Ω3; etc.

So, ψ1(Ωω + 1) is ordinal of cardinality Ω:
 * Ω ≤ ψ1(Ωω + 1) < Ω2

I suppose that
 * ψ1(Ωω + 1) = ωψ1(Ωω) + 1 = ψ1(Ωω)ω

(I'm not sure)