Endre Tóth (SZTE): Burle's theorem: the clones containing every unary operation

University of Szeged, Bolyai Institute, Algebra Seminar

Abstract. In 1959 Ju. I. Janov and A. A. Mucnik showed that on a finite set with at least 3 elements there are continuum many clones. Therefore, describing all clones at once proves to be a difficult problem, and thus mathematicians usually investigate only certain classes of clones. One such class is the class of clones that contain every unary operation; this class was described by G. A. Burle in 1967. Interestingly, these clones form a chain, and this chain is of finite height. This implies that for any finite set A, the clone lattice on A is of finite height. Endre Toth will present the proof of Burle's theorem as part of the clone theory PhD course (MDPT3105).