User blog comment:P進大好きbot/First Order Theory beyond Higher Order Set Theory/@comment-44466522-20200108192317/@comment-35470197-20200108224724

I do not know. At least, T does not imply the Grothendieck universe axiom, i.e. the properness of the class of inaccessibles. When we work with uncomputable large number, the strength itself is not so important, as I explained in Embedding section.