Dualisability of partial unars

Abstract

The dualisability of partial algebras is a largely unexplored area within natural duality theory. This paper considers the dualisability of finite structures that have a single partial unary operation in the type. We show that every such finite partial unar is dualisable. We obtain this result by showing that the relational structure obtained by replacing the fundamental operation by its graph is dualisable. We also give a finite generator for the class of all disjoint unions of directed trees up to some fixed height, considered as partial unars.