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.

The paper can be downloaded here.

Consequence of compactness in Lukasiewicz first order logic

The Los-Tarski Theorem and the Chang-Los-Susko Theorem, two classical results in Model Theory, are extended to the infinite-valued Lukasiewicz logic. The latter is used to settle a characterisation of the class of generic structures introduced in the framework of model theoretic forcing for Lukasiewicz logic .

Consequence of compactness in Lukasiewicz first order logic

Forcing in Lukasiewicz Predicate Logic

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\(\forall\).

Forcing in Lukasiewicz Predicate Logic