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Unravelling Cyclic First-Order Arithmetic
Graham E. Leigh, Dominik Wehr
https://arxiv.org/abs/2507.20865 https://arxiv.org/pdf/2507.20865

Unravelling Cyclic First-Order Arithmetic
Cyclic proof systems for Heyting and Peano arithmetic eschew induction axioms by accepting proofs which are finite graphs rather than trees. Proving that such a cyclic proof system coincides with its more conventional variants is often difficult: Previous proofs in the literature rely on intricate arithmetisations of the metamathematics of the cyclic proof systems. In this article, we present a simple and direct embedding of cyclic proofs for Heyting and Peano arithmetic into purely inductive…