A modal sequent calculus for a fragment of arithmetic

Studia Logica 39 (2-3):245-256 (1980)
Abstract
Global properties of canonical derivability predicates in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, interpolation and the fixed point theorem.
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DOI 10.1007/BF00370323
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Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
The Modal Logic of Provability. The Sequential Approach.Giovanni Sambin & Silvio Valentini - 1982 - Journal of Philosophical Logic 11 (3):311 - 342.
Modal Tableau Calculi and Interpolation.Wolfgang Rautenberg - 1983 - Journal of Philosophical Logic 12 (4):403 - 423.
The Bounded Proof Property Via Step Algebras and Step Frames.Nick Bezhanishvili & Silvio Ghilardi - 2014 - Annals of Pure and Applied Logic 165 (12):1832-1863.

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