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

摘要

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.