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arXiv · 1805.06763

The $Σ_1$-Provability Logic of HA*

Mohammad Ardeshir·Mojtaba Mojtahedi
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Abstract

For the Heyting Arithmetic HA, HA* is defined as the theory $\{A\mid {\sf HA}\vdash A^{\Box}\}$, where $A^{\Box}$ is called the box translation of $A$. We characterize the $Σ_1$-provability logic of HA* as a modal theory ${\sf iH}_σ^*$.

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Mohammad Ardeshir, Mojtaba Mojtahedi. 2018-08-27. The $Σ_1$-Provability Logic of HA*. https://arxiv.org/abs/1805.06763

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