User blog comment:Wythagoras/My Turing machines/@comment-6768393-20131012123348/@comment-1605058-20131013120959

Welp, I thought that when you said "might" you meant that you think it actually does, just like Taranovsky thinks he made such notation.

Every recursive ordinal is describable by Turing machine. What you probably meant is ordinal which we get by collapsing indescribable cardinal. I'm not collapsing function expert, so I won't comment that.