User blog comment:Billicusp/So I don't know if anybody noticed.../@comment-27173506-20160318160910/@comment-27513631-20160324114809

Okay, it is possible to use \(\psi_M\) inplace of \(\chi\), but unless the restriction of \(\gamma<\alpha\) is lifted for \(\psi_M(\gamma)\) in the construction of the function, the notation is effectively limited at \(\psi_{\Omega_1}(M)\). Given the number of modifications already needed, the \(\psi_M\)/\(\chi\) function may as well be separate.

Anyway, I find it much more likely for Hollom to actually mean \(\psi(\chi(M^M))\) etc. than \(\psi(M^M)\) - the notation required is simpler and easier to use, and he didn't give much reasoning in his analysis anyway, or any mention of the \(\chi\) function. That would put it below \(\psi(M)\), assuming he listed up to the limit of his notation.