Galois theory for semiclones

Abstract

We present a Galois theory connecting finitary operations with pairs of finitary relations one of which is contained in the other. The Galois closed sets on both sides are characterised as locally closed subuniverses of the full iterative function algebra (semiclones) and relation pair clones, respectively. Moreover, we describe the modified closure operators if only functions and relation pairs of a certain bounded arity, respectively, are considered.