Geometrical dualities for Łukasiewicz logic

The 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.