User blog comment:PsiCubed2/For Newbies (and Veterans too): The Great Scale of Googology/@comment-25337554-20171220040447/@comment-30754445-20171220042343

Yup.

We could easily have "transwarp", though. If you like, you could say that the range beyond 500 corresponds to actual ordinals (not "ordinal levels" but the transfinite numbers themselves!).

Given that 500 is already the limit of all finite numbers (ω), we might say that 501 is ω+1 and so on... But then it will no longer be scale of numbers only, which kinda goes against the spirit of the whole thing (though such an extended list might still be useful, for example, in teaching people about OCF's).