User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-11227630-20131105084532/@comment-10429372-20131106153925

Your extension is exactly what I meant below.

ψ(ψχ(M 2) (0)) expands to ψ(ψχ(I I ... I I M+1   ) (0))