The $Σ_1$-Provability Logic of HA*

Mohammad Ardeshir, Mojtaba Mojtahedi

Published 2018-05-12Version 1

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 ${\sf iH}_\sigma^*$.