User blog comment:Emlightened/Early Birthday Present For Deedlit/@comment-5529393-20170730212008/@comment-27513631-20170805221009

Sorry for the late reply; I went to check how that worked and then forgot about the tab.

If we have a collapsing function that collapses to \(|\Omega|\), then we might or might not need to be able to do that, but we may as well assume we do, or we don't have such a function.

In that case, we would probably want to collapse into sets \(\{\Psi(alpha+\beta):\beta<\Omega\}\) with \(\text{cof }\alpha \geq \Omega^+\). I don't know how this would generalise to cardinals above \(\Omega^+\), but I doubt that it's efficient to just continue as with \(\Omega^+\)...