Finitely Generated Maximal Partial Clones and Their Intersections

Let A be a finite non-singleton set. For |A| = 2 we show that the partial clone consisting of all selfdual 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| ≥ 3 we show that there are pairs of finitely generated maximal partial clones whose intersection is a not finitely generated partial clone on A.