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

The fact that we take the limsup over all ordinals less than alpha is quite inconvenient - if for the ordinal alpha = w^(n+1) we took the limsup over ordinals of the form w^n * m, than I could create an ITTM of length w^w without too much trouble. As it is, though, any "flashing" will persist in later ordinal stages, so I'm kind of stymied at the moment so far as w^w is concerned.