User blog comment:P進大好きbot/What is the greatest ordinal notation now?/@comment-1605058-20180623095923/@comment-35470197-20180623135054

> The other definition you mention, p進大好きbot it's equal to \(\omega\) for every consistent T.

Why \(\omega\)? The proof theoretic ordinal (in the sense of the consistency) of PA is \(\epsilon_0\) but not \(\omega\) by Gentzen's proof reduction.