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. 
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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/

[1] Aguzzoli S., A note on the representation of McNaughton lines by basic literals, Soft Comput., 2 (1998), 3, 111-115.

[2] Bigard A., K. Keimel and S. Wolfenstein, Groupes et anneaux réticulés, Lecture Notes in Mathematics, Vol. 608, Springer-Verlag, Berlin, 1977. | MR

[3] Burris S. and H. P. Sankappanavar, A course in universal algebra, vol. 78 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1981. | MR | Zbl

[4] Chang, C. C., Algebraic analysis of many valued logic, Trans. Amer. Math. Soc, 88 (1958), 467-490. | DOI | MR | Zbl

[5] Chang C. C., A new proof of the completeness of the Łukasiewicz axioms, Trans. Amer. Math. Soc., 93 (1959), 74-80. | DOI | MR | Zbl

[6] Cignoli R. L. O., I. M. L. D'Ottaviano and D. Mundici, Algebraic foundations of many-valued reasoning, vol. 7 of Trends in Logic-Studia Logica Library, Kluwer Academic Publishers, Dordrecht, 2000. | DOI | MR

[7] Engelking R., General topology, vol. 6 of Sigma Series in Pure Mathematics, second edn., Heldermann Verlag, Berlin, 1989. | MR

[8] Erné M., J. Koslowski, A. Melton and G. E. Strecker, A primer on Galois connections, in Papers on general topology and applications (Madison, WI, 1991), vol. 704 of Ann. New York Acad. Sci., New York Acad. Sci., New York, 1993, pp. 103-125. | DOI | MR

[9] Johnstone P. T., Stone spaces, vol. 3 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1986. | MR | Zbl

[10] Marra, V. and L. Spada, Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras. Annals of Pure and Applied Logic, 164 (2013), 192-210, doi: 10.1016/j.apal.2012.10.001. | DOI | MR | Zbl

[11] Marra V., and L. Spada, The dual adjunction between MV-algebras and Tychonoff spaces, Studia Logica, 100 (2012), 1-26. | DOI | MR | Zbl

[12] Mundici D., Advanced Łukasiewicz Calculus and MV-algebras, vol. 35 of Trends in Logic-Studia Logica Library, Springer, New York, 2011. | DOI | MR | Zbl

[13] Rourke C. P. and B. J. Sanderson, Introduction to piecewise-linear topology, Springer-Verlag, Berlin, 1982. | MR | Zbl

[14] Stone M. H., The theory of representations for Boolean algebras, Trans. Amer. Math. Soc., 40 (1936), 1, 37-111. | DOI | MR | Zbl

[15] Stone M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 3, 375-481. | DOI | MR | Zbl