It is well-known that $\mathbf{PRA}$ plus $\epsilon_0$-induction cannot prove all $\mathbf{PA}$ theorems ([essentially because the former is finitely axiomatizable while the latter isn't][1]). Are there any concrete examples known (preferable "natural")?

(This is an exact copy of [my question on MSE][2], but I expect I won't get any answer there, so I hope I'm allowed to cross-post it here)


  [1]: https://math.stackexchange.com/questions/3130538/how-do-we-know-pa-is-incomparable-with-pra-epsilon-0
  [2]: https://math.stackexchange.com/questions/3769889/concrete-examples-of-statements-not-provable-in-pra-epsilon-0-induction-tha