User blog comment:Ubersketch/Lexicographic ordinal notation up to the Bachmann-Howard ordinal/@comment-30869823-20190913225449/@comment-39541634-20190914195946

The limit that Fejfo has mentioned "(ψ(Ω*ω)") is nothing more than εω.

Also, if you're looking for a nice simple lexicographic ordering that reaches the BHO, then we already have one: The Pair Sequence System. Yes, I know it is technically a number notation, but it can easily be modified to become an ordinal notation, and the "lexicographic ordering" criterion is already built into the notation from the start.