A preliminary study of MV-algebras with two quantifiers which commute
In this paper we investigate the class of MV-algebras equipp ed with two quantifiers which commute as a natural generalization of diagonal free two dimensional cylindric álgebras (see ). In the 40s, Tasrki first introduced cylindric algebras in order to provide an algebraic apparatus for the study of classical predicate calculus. The diagonal free two dimensional cylindric álgebras is a special cylindric algebra. The treatment here of MV-algebras is done in terms of implication and negation. This allows us to simplify some results due to Di Nola and Grigoliain  related to the characterization of a quantifier in terms of some special sub-algebra associated to it. On the other hand, we present a topological duality to this class of algebras and we apply it to characterize the congruences of one algebra vi a certain closed sets. Finally, we study the subvariety of this class generated by a chain of length n + 1 (n <)(BMVn+1). We prove that the subvariety is semisimple and we characterize theirsimple algebras. Using a special functional algebra, we determine all the simple finitealgebras of this subvariety,these results show us that de ordered algebraic structure of BMVn+1 is more complex than to monadic MV-algebra generated by an (n+1)-chain.