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Jori
Jori
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It is well-known that $\mathbf{PRA}$ plus $\epsilon_0$-induction on bounded formulas cannot prove all $\mathbf{PA}$ theorems (essentially because the former$I\Sigma_1$ plus $\epsilon_0$-induction on bounded formulas is finitely axiomatizable while the latter isn't). Are there any concrete examples known (preferable "natural")?

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

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). Are there any concrete examples known (preferable "natural")?

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

It is well-known that $\mathbf{PRA}$ plus $\epsilon_0$-induction on bounded formulas cannot prove all $\mathbf{PA}$ theorems (essentially because $I\Sigma_1$ plus $\epsilon_0$-induction on bounded formulas is finitely axiomatizable while the latter isn't). Are there any concrete examples known (preferable "natural")?

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

Source Link
Jori
Jori
  • 189
  • 8

Concrete examples of statements not provable in PRA + $\epsilon_0$-induction that are provable in PA?

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). Are there any concrete examples known (preferable "natural")?

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