Natural Dualities for Varieties of MV-Algebras, I

MV-algebras are the Lindenbaum algebras for Łukasiewicz’s infinite-valued logic, just as Boolean algebras correspond to the classical propositional calculus. The finitely generated subvarieties of the variety M of all MV-algebras are generated by finite chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite chain, and use it to describe the free and the injective members of these classes. Finally, we point out the relations between the dualities and some categorical equivalences discovered by A. Di Nola and A. Lettieri.