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arXiv · 2606.07166

Cyclic proofs in the equational version of Primitive recursive arithmetic

Daniyar Shamkanov
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Abstract

In this brief note, we present a cyclic proof system developed specifically for the equational version of Primitive recursive arithmetic and establish the equivalence of the two systems. A distinctive feature of our approach is that it does not rely on automata-theoretic methods but is implemented primarily using the tools of structural proof theory.

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Daniyar Shamkanov. 2026-06-05. Cyclic proofs in the equational version of Primitive recursive arithmetic. https://arxiv.org/abs/2606.07166

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