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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2014
- DOI:
- 10.48550/arXiv.1409.4601
- arXiv:
- arXiv:1409.4601
- Bibcode:
- 2014arXiv1409.4601B
- Keywords:
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- Mathematics - Logic;
- Computer Science - Computational Complexity;
- Computer Science - Logic in Computer Science;
- Mathematics - Rings and Algebras
- E-Print:
- 13 pages