User blog comment:TheKing44/Grand Finale Functions/@comment-35470197-20190611051239/@comment-39605890-20190611093913

I was just noting that for people unfamiliar with Rayo's function, as a way of motivating my functions. I know that Rayo knew that his function was not expressible in first order set theory.

Also, I think that the fact that Rayo's function is definable in MK is a good illustration of the terminology issue. Rayo says that his function grows faster than any function definable in first order set theory, yet you say that it is definable in MK. Who is right? The answer is you both are; you're just using the term "first-order set theory" in different ways. You seem to be defining it as the language of first-order logic, along with the $$\in$$ symbol. Rayo defines it as the theory of $$(V, \in)$$.