Embedding Gödel propositional logic into Prior's tense logic

The well-known Goedel translation embeds intuitionistic propositional logic into the modal logic S4. In this note, we use essentially the same translation to embed Goedel infinitevalued propositional logic into a schematic extension of Prior’s bimodal tense logic that allows finite chains only as flows of time. While our proofs use elementary techniques in many-valued algebraic logic, our embedding is strongly related to well-known results from the theory of modal companions to superintuitionistic logics. For the reader’s convenience we include a short discussion of the latter results.