On Gentzen Systems Associated with the Finite Linear MV-algebras

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Abstract
In this paper we obtain a characterization of the algebraizability of an m-dimensional Gentzen system in line with the characterization obtained for m-dimensional deductive systems and the characterization of 2-dimensional Gentzen systems. We also prove that if S(m) is the finite linear MV-algebraof m elements, then the m-dimensional Gentzen system obtained by using the sequent calculi associated with S(m) is equivalent to the m-valued Łukasiewicz logic Łm and to the equational consequence relation associated with S(m). Taking the two-element Boolean algebra we obtain the expected result concerning the relationship between the sequent calculus LK, the Classical Prepositional Calculus and the variety of Boolean algebras.

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