User blog comment:Plain'N'Simple/A question for proof-theory experts/@comment-35392788-20191029194318/@comment-35392788-20191030153853

Typo fixed.

I don't really understand your last point however. It might be very much true that \(\varepsilon_0[n]\) can be proven total in PA, but transfinite induction along \(\varepsilon_0\) is still not provable in PA. Though, maybe the equivalence I proposed should rather be an implication.