User blog comment:TheKing44/Grand Finale Functions/@comment-35470197-20190611051239/@comment-35470197-20190611090822

I see. By the way, as I have already pointed out here, Rayo's number itself is not regarded as googology in first order set theory. Therefore your proposal "it would be incorrect that this function settles Googology in first-order set theory" is a little misleading as if it were regarded as googology i first order set theory.

Also, your anothe proposal "It would only be fair to compare it to other functions in second-order set theory. " is not reasonable because Rayo's number can be beaten by an analogous number defined in MK, which is a first order set theory which is able to define truth predicate at \(V\). Remember that we usually compare second order arithmetics and first order set theory. The point which we should care to be fair is not the order of the formal logic, but is the proof theoretic strength and presentability.