Semirigidity problems in k-valued logic

The study of semirigid sets arose from the classification of bases. In this complex problem-fully solved only for |A|=2, 3-one of the task is to find all minimal nontrivial intersections of systems of maximal clones. Most of the clones are determined by reflexive relations (binary or of higher arities) and so we need to determine subsets R of these relations such that every function preserving all relations in R is either constant or is a projection. In this paper we give a short overview of this problem for 1) isotone relations, 2) central relations and 3) quasi-linear relations. Finally we add some new results for 4) autodual clones