User blog comment:Boboris02/Ordinal Analysis of Theories/@comment-11227630-20180213035846/@comment-1605058-20180214133528

Sorry if I distracted the conversation from its main point, just wanted to point out what you've said isn't quite correct. But the bottom line cannot be argued with - Taranovsky's notation is a recursive one, hence, by the very definition, if a theory proves it well-founded, the theory ought to have PTO larger than the order's length.