User blog comment:King2218/FGH Things/@comment-5029411-20140304234740/@comment-24509095-20140305061540

But wait ... you turned the ordinal into a function.

I should add

f[l]^m(n) = f[l][l]...m [l]'s...[l][l](n)

Therefore, the third hierarchy ordinal should probably be

d = f[w]^{f[w]^{f[w]^{...}(w)}(w)}(w)

which has the property:

d = f[w]^d(w)

I'll be adding the 4th and the 5th one today too :P