Projective clone homomorphisms
  It is known that a countable $\omega$-categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone homomorphism. We investigate the relationship between the existence of a clone homomorphism to the projection clone, and the existence of such a homomorphism which is continuous and thus meets the above criterion. 
Manuel Bodirsky, Michael Pinsker, Andr\'as Pongr\'acz
math.LO cs.CC cs.LO math.RA