We prove that the $n$-generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the $n$-generated free MV$^{(n)}$-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV${}^{(n)}$-algebras…
Recently an expansion of logic with fixed points has been considered. In the present work we study the algebraic semantics of this logic, namely algebras, from algebraic, model theoretic and computational standpoints. We provide a characterisation of free algebras as…
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…
In this paper we study the notion of forcing for Lukasiewicz predicate logic (L, 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…
We study a system, $\mu$L$\Pi$, obtained by an expansion of L$\Pi$ logic with fixed points connectives. The first main result of the paper is that $\mu$L$\Pi$ is standard complete, i.e. complete with regard to the unit interval of real numbers…