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A Modal Sequent Calculus for a Fragment of Arithmetic

G. Sambin and S. Valentini
Studia Logica: An International Journal for Symbolic Logic
Vol. 39, No. 2/3 (1980), pp. 245-256
Published by: Springer
Stable URL: http://www.jstor.org/stable/20014984
Page Count: 12
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A Modal Sequent Calculus for a Fragment of Arithmetic
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Abstract

Global properties of canonical derivability predicates (the standard example is Pr() 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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