User blog comment:Emlightened/Early Birthday Present For Deedlit/@comment-5529393-20180611201219

A couple of things:

Is Psi(Omega+) really the first weakly Mahlo cardinal? How would one go about showing that?

I've been trying to extend your OCF to a full notation for countable ordinals, but I'm having trouble. We need to be able to collapse to various tiers (e.g. collapsing some function of a 3-Mahlo cardinal to a 2-Mahlo one), so it looks like we would need to define the Mahlo hierarchy, like how it is done in the weakly compact notation. But, then the advantage of using this notation goes away it seems.