User blog comment:PsiCubed2/For Newbies (and Veterans too): The Great Scale of Googology/@comment-32876686-20171216155134/@comment-30754445-20171216174525

Yeah, since my current educated guess level 100 is the relatively tame Γ0, it is obvious the scale would need more than 100 levels.

I've already mentioned, in my reply to Nayuta Ito, that doing a "scale of 10's" gives a nice big picture... but for the really big guns, we might consider a "scale of 100's". Perhaps something like this:

000-099 Up to Γ0

100-199 Up to ψ(ψɪ(0))

200-299 Up to 2nd order arithmetic

300-399 Up to the limit of computable functions

400-499 Busy Beavers and variations (including oracles)

500-599 Rayo and variations

600+ Reserved for stuff that haven't been invented yet

(boy, now it really starts to look like a Dewey classification system, doesn't it...)

Or alternatively, we could condense the entire scale to asymptotically diverge at 100, with Γ0 being downgraded to (say) 90 and using decimals as you suggested.

What would the people here prefer? Suggestions would be most welcome.