User blog comment:KthulhuHimself/Norminals Revisited./@comment-5529393-20160710171207/@comment-5529393-20160711164335

Unfortunately, I don't; I mean, you can of course extend past the particular case of N<<...<0,1>,1>,...,1>, but I don't know how this continues, and saying "it quantifies over anything using  at all" is too vague.

The new definition doesn't work because you use <0,2> in the definition of <0,2>. Adding "<" and ",1>" to the language still doesn't seem to break out of the aforementioned limit.