2025/05/16 by Marco Abbadini, Abbadini, Marco, Adam Přenosil +1
Computer Science · Decision Sciences · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2505.11490
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 the existing duality of Cignoli and Marra or locally weakly finite MV-algebras and to extend it to a corresponding class of positive MV-algebras, in this paper we investigate Stone-like dualities where the algebra L is allowed to be infinite. This requires restricting our attention from the whole prevariety generated by L to the subclass of algebras representable as algebras of L-valued functions of finite range, a distinction that does not arise in the case of finite L. Provided some requirements on L are met, our main result establishes a categorical duality for this class of algebras, which covers the above cases of MV-algebras and positive MV-algebras.