Projective clone homomorphisms

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.

13 pages

References in corpus (3)

• A universal-algebraic proof of the complexity dichotomy for Monotone Monadic SNP
• Uniform Birkhoff
• Topology is relevant (in a dichotomy conjecture for infinite-domain constraint satisfaction problems)

Cited by in corpus (6)

• Polish topologies on endomorphism monoids of relational structures
• Topology is relevant (in a dichotomy conjecture for infinite-domain constraint satisfaction problems)
• Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones
• Twenty years of Nešetřil's classification programme of Ramsey classes
• 1-in-3 vs. Not-All-Equal: Dichotomy of a broken promise
• On a stronger reconstruction notion for monoids and clones