Natural duality for finitely valued algebras - Marco Abbadini

The theory of natural dualities provides a well-developed framework for studying Stone-like dualities induced by an algebra L, which acts as a dualizing object when equipped with suitable topological and relational structure. The development of this theory has, however, largely remained restricted to the case where L is finite. Motivated by the desire to provide a universal algebraic formulation of Cignoli and Marra's duality for locally weakly finite MV-algebras and to extend it to a corresponding class of positive MV-algebras, we investigate Stone-like dualities with L possibly infinite. This requires a restriction from the whole prevariety generated by L to the subclass of algebras representable as algebras of L-valued functions of finite range, a distinction not arising when L is finite. Under some conditions on L, our main result establishes a categorical duality for this class of algebras, covering the above cases of MV-algebras and positive MV-algebras.