Proof schemata simulate primitive recursive arithmetic only when the induction variable is not strongly quantified, so the abstract's unqualified claim is not supported by the paper's own results.
Theoretical Computer Science 403(2-3), pp
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Towards an Analysis of Proofs in Arithmetic
Proof schemata simulate primitive recursive arithmetic only when the induction variable is not strongly quantified, so the abstract's unqualified claim is not supported by the paper's own results.