Finitely Generated Maximal Partial Clones and Their Intersections

Abstract

Let $A$ be a finite non-singleton set. For $|A|=2$ we show that the partial clone consisting of all self-dual monotonic partial functions on $A$ is not finitely generated, while it is the intersection of two finitely generated maximal partial clones on $A$. Moreover, for $|A| \ge 3$ we show that there are pairs of finitely generated maximal partial clones whose intersection is a not finitely generated partial clone on $A$.