Arithmetical Completeness Theorem for Modal Logic $$\mathsf{}$$ |
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Authors: | Taishi Kurahashi |
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Institution: | 1.Department of Natural Sciences,National Institute of Technology, Kisarazu College,Kisarazu, Chiba,Japan |
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Abstract: | We prove that for any recursively axiomatized consistent extension T of Peano Arithmetic, there exists a \(\Sigma _2\) provability predicate of T whose provability logic is precisely the modal logic \(\mathsf{K}\). For this purpose, we introduce a new bimodal logic \(\mathsf{GLK}\), and prove the Kripke completeness theorem and the uniform arithmetical completeness theorem for \(\mathsf{GLK}\). |
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