User blog comment:Googleaarex/My number is bigger! (Googology Wiki version)/@comment-2033667-20140919220815/@comment-2033667-20140919231106

let me clarify. since i suck at set theory it probably doesn't work.

in first-order set theory, we can identify variables using  x' x x' x' x''  etc. each variable is a set.

in second-order set theory, we have all of the above variables (which are sets) and the variables  xx' xx'' xx xx'  etc. which are all classes.

in third-order set theory, we have the x and xx variables, plus  xxx' xxx'' xxx xxx'  etc. the xxx variables are collections of classes (is that a thing?).

the pattern is obvious from here.