Rosenberg-Type Completeness Criteria for Subclones of Slupecki´s Clone

We describe all clones on a finite set with at least three elements, which are maximal for the property of not containing all non surjective operations. We deduce Rosenberg-type completeness criteria for every sub clone of Slupecki´s clone that contains all non surjective operations. As another application, we find all sub clones of Slupecki´s clone for which the associated R-relation has only finitely many classes.