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Let $PA_{\omega}$ be just like $PA$ except that $PA_{\omega}$-proofs can use any number of applications of the recursive $\omega$-rule. The recursive $\omega$-rule allows the following: For each ...

Hello. I already asked the question here. The main point is that I tried to prove in Primitive recursive arithmetic (PRA) the totality of the Ackerman function, and I found, that the single thing ...