User blog comment:TheKing44/Grand Finale Functions/@comment-35470197-20190611051239/@comment-35470197-20190611102037

> Rayo says that his function grows faster than any function definable in first-order set theory

Oh, I did not know the statement. Could you give me a source?

> The answer is you both are; you're just using the term "first-order set theory" in different ways.

Maybe true. I note that Rayo himself is not a professional mathematician, and hence the terminology can be irregular. Another issue is that he has never declared what (first and second order) axioms he used. I guess that he meant that it can never be the segment of his (unspecified) set theory given by forgetting all the second order axioms.

> it calls Rayo's definition of first-order set theory FOST

No. It just calls the language of first-order set theory FOST. Read the explanation in the other section.