Restriction-Closed Hyperclones

Abstract

The sets of multi-valued operations closed with respect to compositions and restrictions, called restriction- closed hyperclones, defined on the finite set E(k)={0, 1,..., k-1} (kges2) are investigated. The set of all maximal restriction-closed pre-hyperclones (composition without projections) is obtained. Based on it the analogue of Slupecki completeness criteria in restriction-closed pre-hyperclones is established. Next the problem of classification of restriction-closed hyperclones according to their single-valued clone component is considered.