Polymorphism clones of homogeneous structures: generating sets, Sierpiński rank, cofinality and the Bergman property

Abstract

© 2018, Springer International Publishing AG, part of Springer Nature. In this paper, motivated by classical results by Sierpiński, Arnold and Kolmogorov, we derive sufficient conditions for polymorphism clones of homogeneous structures to have a generating set of bounded arity. We use our findings in order to describe a class of homogeneous structures whose polymorphism clones have a finite Sierpiński rank, uncountable cofinality, and the Bergman property.