User blog comment:PolyhedralMatrix102/"Bigger" notation/@comment-32783837-20180319182438/@comment-1605058-20180319184118

Actually PTO is always bounded by the CK ordinal, and for some theories (which have been thought of already, for example inconsisent theories) it is equal. Hence ⌇⌇ is the CK ordinal. So in this case it is well-defined, but only because there is a hard limit which has already been reached.