Emergent Mind
Projective clone homomorphisms
(1409.4601)
Published Sep 16, 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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