Data di Pubblicazione:
2012
Citazione:
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.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
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
Elenco autori:
V. Marra, L. Spada
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