User blog comment:Lepton Adapter/Meta: What a growth rate is/@comment-35470197-20181127215527/@comment-35470197-20181128010557

I think that it is incorrect. But I am not sure the precise condition which you are refering to. At least, the "strict increasing" property does not ensure the desired property in FGH.

On the other hand, the "strictly increasing" property ensures it for another specific uncomputable hierarchy which appears in usual mathematics (sorry, I forgot the name). It is used to verify that every countably infinite set of subsets of natural numbers admits a pseudo-intersection. (It roughly corresponds to the fact that every countably infinite set of functions is uniformly bounded by another function with respect to eventual domination.) So I guess that you are refering to another hierarchy. Sorry if I am incorrect.