User blog comment:Nayuta Ito/faketest/e0/@comment-30754445-20180805015451/@comment-35470197-20180805105400

@Rpakr

Does \(\psi_M\) satisfy \(\psi_M(\alpha) = \sup_{\beta < \alpha} \psi_M(\beta)\) in the case where \(\alpha\) is a limit ordinal?

> ψM(α), when cof(α)=M, is a bit complicated. First, define function f to be the function that replaces the last M in α with the input, and calculate it's first fixed point.

What does the last \(M\) in \(\alpha\) mean? Is there a canonical way to express all ordinals \(\alpha\) with \(\textrm{cof}(\alpha) = M\) using \(M\)?