The $Σ_1$-Provability Logic of HA*

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