User blog comment:TheKing44/Grand Finale Functions/@comment-35470197-20190611051239/@comment-35470197-20190611134351

> The article Rayo's number makes that claim.

Could you tell me what sentence in the article makes that claim? I will edit the article, because the article is a little old. (For example, the article states that BIG FOOT surpasses Rayo's number, but it is false.)

> In this sense, MK and NBG are essentially second-order set theories since they can quantify over predicates and functions over V.

Right. (I note that there is also second order NBG, which is not the same as NBG. Therefore regarding them as second order set theory could cause confusion, even though they are very similar to second order set thoery.)

> the axioms Rayo was thinking of were second-order ZFC or something

Maybe true. Or Rayo might not be interested in an explicit choice of formal theory.