User blog comment:Ubersketch/A proposal for a standard/@comment-35470197-20190811012241/@comment-39541634-20190812064156

> If people in this community rarely worked on ordinal beyond an ordinal X ... Maybe X is something like ψ(Ω_ω) for the current community, because I have never seen a completely well-defined large number which has been verified to go beyond that level other than variants of BMS this year.

IMO the fact that 99% of the "work" here beyond ψ(Ω_ω) is ill-defined (or a the very least - insufficiently justified) is precisely the reason this community needs a standard notation for these levels.

I maintain that having a standard notation which is:

(1) Well-defined

(2) Verified to work in precisely the way it is intended to work

(3) Agreed upon as the sole standard by which other notations (both ordinal and googological) are measured.

(4) Agreed upon as required knowledge before people make claims and analyses at the given level.

would do wonders to eliminate 90% of the nonesense we see here so often.

I do agree that there comes a point, much later, where having a standard notation would be useless. Basically, when we reach two conceptual levels above the stuff that the people here sort-of understand, it would be a good time to stop. For example, there's absolutely no point in trying to create a standard notation for weakly-compact collapse when the people here are having trouble formalizing even the simplest OCFs.

Perhaps a good cut-off point for now would be ψ(the 1st Omega fixed point), which this wiki likes to call ψ(ψ_I(0)) for some reason. You can get there without adding anything new to the familiar ψ's and Ω's, yet the extention of simple OCFs to this level is not trivial.