User blog comment:P進大好きbot/Analysis of 非想非非想 notation/@comment-39253344-20190806190108/@comment-35470197-20190806222227

Every countable notation equipped with a well-founded partial ordering, i.e. a \(<\)-relation which allows us to define FGH, has a limit, which is a countable ordinal. Exactly, nobady can cheat like that. Something like "biggest countable ordinal" and "biggest recursive ordinal" describable in \(n\) symbols is invalid because of Berry's paradox.