The lattice of clones of self-dual operations collapsed

We prove that there are continuum many clones on a three-element set even if they considered up to homomorphic equivalence. The we use this fact consisting of self-dual operations, i.e. operations preserve the relation [Formula: see text]. However, only countably such when equivalence with respect minor-preserving maps instead clone homomorphisms. give full description ordered by existence maps. Our result can also be phrased as statement about structures set: containing text], primitive positive constructability, because is map from polymorphism finite structure text] and construction in