User blog comment:Ynought/What grows faster?/@comment-37246647-20190314233119/@comment-35470197-20190314234839

"Ordinals provable under ZFC" does not make sense, because ordinals are not sentences. Further, the ability to express ordinals are irrelevant to the required axioms. For example, several ordinal notations with large cardinals are well-defined under ZFC.

I guess that you understand what ordinals mean, but many googologists do not. Therefore it is better to state more clearly so that the assertion causes no misunderstandings on ordinalls by beginners.