User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 3/@comment-5529393-20130530121945/@comment-5529393-20130530155727

Look at it this way. We have the regular psi notation, which I will call the "strong" psi notation. We can also define a "weak" psi notation, where we have all the cardinals up to \(\Omega_{\omega}\), but we just have \(\psi_0\) - no collapsing at higher levels. Obviously this is a much weaker notation the the strong psi notation.

According to you, (k+1)-brackets are the equivalent of \(\Omega_k\). But in which notation? They both have \(\Omega_k\) in them, and in both cases you have the phenomenon that the \(\Omega_k\) represent fixed points. How do you justify one over the other?

My point is a general similarity is not enough to justify an exact matchup. More detailed analysis needs to be done.