The dual adjunction between MV-algebras and Tychonoff spaces
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 aduality 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
The unification type of Łukasiewicz logic is nullary
This is the most updated version of a talk presenting the result contained here. The talk was given in plenary session at Topology, Algebra, and Category in Logic -TACL- V, Marseille, 28$^{th}$ July. 2011
The unification type of Łukasiewicz logic is nullary
