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Projective clone homomorphisms (1409.4601v3)
Published 16 Sep 2014 in math.LO, cs.CC, cs.LO, and math.RA
Abstract: 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.
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