User blog comment:LittlePeng9/ITTM galore/@comment-5529393-20140318210326/@comment-1605058-20140318211703

I already have an idea on how a machine can clock \(\omega^\omega\): first cell is going to be a master flag, and after that we will have pairs of cells - first in a pair says "we were here already" and second is flashing flag. We flash the first of the flags and, when we flash it infinitely many times, we go flash second flag. After second flag flashes infinitely many times, we go to third one etc. If we flash some cell for the first time we mark "we were here" and go flash master flag. With proper machine we see that master flag will flash around w, w^2, w^3, w^4 etc. so at w^w we'll be ready to halt. We need, of course, a bit of work on details, like making machine go exactly to master flag, but I'll work on it tomorrow.