Intersections of isotone clones on a finite set

Let <or= be a fixed order of height at least 2 on a set A (i.e. contains a chain a<b<c). It is shown that all the isotone clones preserving orders on A isomorphic to <or= intersect in the clone K/sub A/ of trivial functions (i.e. all the projections and all the constant operations on A). It is further shown that for A finite with at least eight elements and for any six-element set there exist two orders on A such that every joint endomorphism is trivial (i.e. id/sub A/ or constants). The same is true for intersections of isotone clones. This yields that with the above restrictions there are four maximal isotone clones intersecting in K/sub A/. Separate considerations are given on the intersections of maximal isotone clones for mod A mod =3 and 4.<<ETX>>