User blog comment:Boboris02/Ordinal Analysis of Theories/@comment-11227630-20180213035846/@comment-1605058-20180214103531

@Boboris02 Correction: PTO is the least ordinal \(\alpha\) such that, for any recursive well-order \(R\) of length \(\alpha\), which ought to be explicitly given by a Turing machine or something equivalent, T is not able to prove \(R\) is a well-order. T doesn't have to prove the ordering is recursive, since it is already given as such.