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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In memoriam Leo Esakia
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Marra, V., Spada, L. The Dual Adjunction between MV-algebras and Tychonoff Spaces. Stud Logica 100, 253–278 (2012). https://doi.org/10.1007/s11225-012-9377-z
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DOI: https://doi.org/10.1007/s11225-012-9377-z