User blog comment:Nayuta Ito/A simple way to compare ordinals/@comment-1605058-20150331145509/@comment-2033667-20150331165223

The definition of FGH would hold that \(f_1(\omega) = f_0^\omega(\omega)\). It's not hard to agree on a definition of transfinite function iteration that has this equal to \(\sup \{f_0^n(\omega) : n < \omega\} = \(\sup \{\omega + n : n < \omega\} = \omega 2\).

I don't think this result generalizes well at all, however.