Syntactical results on the arithmetical completeness of modal logic

Studia Logica 52 (4):549 - 564 (1993)
In this paper the PA-completeness of modal logic is studied by syntactical and constructive methods. The main results are theorems on the structure of the PA-proofs of suitable arithmetical interpretationsS of a modal sequentS, which allow the transformation of PA-proofs ofS into proof-trees similar to modal proof-trees. As an application of such theorems, a proof of Solovay's theorem on arithmetical completeness of the modal system G is presented for the class of modal sequents of Boolean combinations of formulas of the form p i,m i=0, 1, 2, ... The paper is the preliminary step for a forthcoming global syntactical resolution of the PA-completeness problem for modal logic.
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DOI 10.1007/BF01053259
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References found in this work BETA
Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
[author unknown] (1988). Self-Reference and Modal Logic. Journal of Symbolic Logic 53 (1):306-309.

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Paolo Gentilini & P. Gentilini (1992). Provability Logic in the Gentzen Formulation of Arithmetic. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):535-550.

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