User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-5150073-20140515153351/@comment-10429372-20140521150525

Okay, I'll try to explain it again, as clear as I can.

Ω is an diagonalizer, beacause it nests the ψ function: ψ(Ω) = ψ(ψ(ψ(...))).

Ω2 is an diagonalizer, beacause it nests the ψ1 function: ψ1(Ω2) = ψ1(ψ1(ψ1(...))).

I is an diagonalizer, beacause it nests the ψI function: ψI(I) = ψI(ψI(ψI(...))).

In general, X is an diagonalizer of the function f if f(X) = f(f(f(...))).