## The dual adjunction between MV-algebras and Tychonoff spaces

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 aduality 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.

The dual adjunction between MV-algebras and Tychonoff spaces

Tags: adjunction, categoricalequivalence, Chang’s completeness theorem, compact Hausdorff spaces, duality, Ho ̈lder’s theorem, Łukasiewicz logic, MV-algebras, piecewise linear maps, rational polyhedra, Tychonoff cube, W ́ojcicki’s theorem, Z-maps

[…] and I have just finished our paper on the connection between natural dualities and the duality between semisimple MV-algebras and compact Hausdorff spaces with definable maps. Actually, we […]

[…] and the category (P_{mathbb{Z}}) of rational polyhedra with (mathbb{Z})-maps (see here), with (1) and (2) to […]

[…] Vincenzo Marra of the University of Milan that was published in Vincenzo Marra and Luca Spada. The dual adjunction between MV-algebras and Tychonoff spaces, Studia Logica 100(1-2):253-278, 2012. Special issue of Studia Logica in memoriam Leo Esakia (L. […]