Oligomorphic clones
A clone on a countable domain is called oligomorphic if its set of permutations forms an oligomorphic permutation group (that is, if it has finitely many orbits of finitary tuples). In this article the authors generalize some fundamental theorems of universal algebra from clones over a finite domain to oligomorphic clones. First, they define minimal oligomorphic clones, and present equivalent characterizations of minimality, and then generalize Rosenberg's five types classification to minimal oligomorphic clones. Also, they present a generalizations of the theorem of Baker and Pixley to oligomorphic clones.
scientific article; zbMATH DE number 5186255