## MV-algebras, infinite dimensional polyhedra, and natural dualities

Leo and I have just finished our paper on the connection between natural dualities and the duality between semisimple MV-algebras and compact Hausdorff spaces with definable maps. Actually, we provide a description of definable maps that is intrinsically geometric. In addition, we give some applications to semisimple tensor products, strongly semisimple and polyhedral MV-algebras.

In this paper we study the notion of forcing for Lukasiewicz predicate logic (L$$\forall$$, for short), along the lines of Robinson’s forcing in classical model theory.We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for L$$\forall$$, while for the latter, we study the generic and existentially complete standard models of L$$\forall$$.