Clones on three elements preserving a binary relation

We describe the clones on 3 elements that can be expressed as Pol ρ for ρ a binary relation. We present the poset of these clones ordered by inclusion. This article is a shortened version of the author’s thesis, to give an idea of the whole work. Presented by R. P?schel. Received March 24, 2005; accepted in final form December 20, 2005.