User blog comment:Ubersketch/Lexicographic ordinal notation up to the Bachmann-Howard ordinal/@comment-35470197-20190913052145/@comment-35470197-20190913142609

@Syst3ms

Oh, the OP gave up to define the conversion from ordinals to strings... I wonder whether he understood what you explained or not.

@Ubersketch

Do you understand that it does not give a well-defined conversion from ordinals to strings even if you have a correspondence from expressions to strings.

By the way, could you please explain what "expression" means in your context? Also, could you quantify \(\alpha\)? You seem first to use it as an ordinal, but secondly to use it as an expression. You could notice your mistake if you quantified it.