# Monadic Intuitionistic and Modal Logics Admitting Provability Interpretations

@article{Brantley2020MonadicIA, title={Monadic Intuitionistic and Modal Logics Admitting Provability Interpretations}, author={Kristi L. Brantley}, journal={The Bulletin of Symbolic Logic}, year={2020}, volume={26}, pages={296 - 296} }

The Gödel translation provides an embedding of the intuitionistic logic IPC into the modal logic Grz, which then embeds into the modal logic GL via the splitting translation. Combined with Solovay’s theorem that GL is the modal logic of the provability predicate of Peano Arithmetic PA, both IPC and Grz admit arithmetical interpretations. When attempting to ‘lift’ these results to the monadic extensions MIPC, MGrz, and MGL of these logics, the same techniques no longer work. Following a…

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