User blog comment:LittlePeng9/FOOT is not as strong as I thought/@comment-5529393-20161225200516

Question: in defining Rayo's number, Rayo took the trouble to formally define it using second order logic. If we define HOSTm(n) to be the largest number definable in n symbols using mth order set theory, is it a simple matter of just going to m+1 order set theory to formally define it?