The $\Sigma_1$-Provability Logic of HA*

Mohammad Ardeshir; Mojtaba Mojtahedi

The $\Sigma_1$-Provability Logic of HA*

Logic 2018-08-28 v3

Authors: Mohammad Ardeshir , Mojtaba Mojtahedi

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 $\Sigma_1$ -provability logic of HA* as a modal theory ${\sf iH}_\sigma^*$ .

Keywords

heyting arithmetic provability logic box translation modal theory sigma_1-provability

Cite

@article{arxiv.1805.06763,
  title  = {The $\Sigma_1$-Provability Logic of HA*},
  author = {Mohammad Ardeshir and Mojtaba Mojtahedi},
  journal= {arXiv preprint arXiv:1805.06763},
  year   = {2018}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1409.5699

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