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.

The Dual Adjunction between MV-algebras and Tychonoff Spaces / V. Marra, L. Spada. - In: STUDIA LOGICA. - ISSN 0039-3215. - 100:1-2(2012), pp. 253-278.

The Dual Adjunction between MV-algebras and Tychonoff Spaces

V. Marra
Primo
;
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.
Łukasiewicz logic; ℤ-maps; adjunction; categorical equivalence; Chang's completeness theorem; compact Hausdorff spaces; duality; Hölder's theorem; MV-algebras; piecewise linear maps; rational polyhedra; Tychonoff cube; Wójcicki's theorem
Settore MAT/01 - Logica Matematica
Settore MAT/02 - Algebra
Settore INF/01 - Informatica
2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/210262
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