The $\Sigma$_1 Provability Logic of HA
Mohammad Ardeshir, Mojtaba Mojtahedi · arXiv (Cornell University) · 2014
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 ${\sf iH}_\sigma^*$.