Geodesic
Geometrical Dualities for Łukasiewicz Logic
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 749-763

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This article develops a general dual adjunction between MV-algebras (the algebraic equivalents of Łukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. Such a dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. Further the duality theorem for finitely presented objects is obtained from the general adjunction by a further specialisation. The treatment is aimed at emphasising the generality of the framework considered here in the prototypical case of MV-algebras. 
@article{BUMI_2013_9_6_3_a17,
     author = {Spada, Luca},
     title = {Geometrical {Dualities} for {{\L}ukasiewicz} {Logic}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {749--763},
     publisher = {mathdoc},
     volume = {Ser. 9, 6},
     number = {3},
     year = {2013},
     mrnumber = {3202853},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a17/}
}
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Spada, Luca. Geometrical Dualities for Łukasiewicz Logic. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 749-763. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a17/