User blog comment:Plain'N'Simple/Letter Notation Up to Z: Outline and mnemonics/@comment-36984051-20191106024302/@comment-39541634-20191106080938

The Ordinal for X is given in the table in my post. It's at the limit of what the best professional set theorists managed to build with an OCF, and even that is in dispute (there's a single peer-reviewed article that claims to reach that high).

So X would outgrow any computable notation we currently have an estimate for. It is, however, divided into sections (X2, X3, X4, ... ) and the lower ones would be easy enough to handle (only problem is that I haven't yet decided how the progression will go, and there are deep reasons for this indecision).

As for BMS:

We don't even know if (0,0,0)(1,1,1)(2,2,0)[n] terminates, so the question is moot.