The Dual Adjunction between MV-algebras and Tychonoff Spaces

Studia Logica 100 (1-2):253-278 (2012)

Abstract

We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result. Our approach develops first a general dual adjunction between MV-algebras and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. Our treatment is aimed at showing exactly which parts of the basic theory of MV-algebras are needed in order to establish these results, with an eye towards future generalisations

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Citations of this work

Algebraic Geometry for Mv-Algebras.Lawrence P. Belluce, Antonio di Nola & Giacomo Lenzi - 2014 - Journal of Symbolic Logic 79 (4):1061-1091.
Germinal Theories in Łukasiewicz Logic.Leonardo Manuel Cabrer & Daniele Mundici - 2017 - Annals of Pure and Applied Logic 168 (5):1132-1151.

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