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Relativised homomorphism preservation at the finite level
[article]
2015
arXiv
pre-print
In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite lattices that are definable by a first-order sentence but not by existential positive sentences, demonstrating the failure of the homomorphism preservation property for lattices at the finite level. In contrast to the negative results for algebras, we establish a
arXiv:1510.05354v1
fatcat:xcmduwitrfgvdjgactxc4a6fnu