User blog comment:Rgetar/Creating FGH for transfinite ordinals/@comment-35470197-20190630215635

The rule \(f_{\alpha}(x) = f_{\alpha[x]}(x)\) for the case \(\textrm{cof}(\alpha) = \Omega\) does not work unless you fix a system of fundamental sequences of length \(\Omega\) for all such \(\alpha\)'s. Unlike the countable case, you do not have a recursive way in arithmetic, and hence it is actually difficult.