A discrete representation of free MV-algebras
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 and special maps between them as morphisms.
A discrete representation of free MV-algebras
Advances in the theory of muLPi algebras
Recently an expansion of \rm L {\rm\Pi\frac{1}{2}} logic with fixed points has been considered. In the present work we study the algebraic semantics of this logic, namely \mu L\Pi algebras, from algebraic, model theoretic and computational standpoints.
We provide a characterisation of free \mu L\Pi algebras as a family of particular functions from [0,1]^{n} to [0,1]. We show that the first-order theory of linearly ordered \mu L\Pi-algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered \rm L {\rm\Pi\frac{1}{2}} algebras. Furthermore, we give a functional representation of any \rm L {\rm\Pi\frac{1}{2}} algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of \mu L\Pi algebras is in PSPACE.
Advances in the theory of muLPi algebras
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
LPi Logic with Fixed Points
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 endowed with a suitable structure.
We also prove that the class of algebras which forms algebraic semantics for this logic is generated, as a variety, by its linearly ordered members and that they are precisely the interval algebras of real closed fields. This correspondence is extended to a categorical equivalence between the whole category of those algebras and another category naturally arising from real closed fields.
Finally, we show that this logic enjoys implicative interpolation.
