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Existential positive types and preservation under homomorphisms
Rossman, B.;
Logic in Computer Science, 2005. LICS 2005. Proceedings. 20th Annual IEEE Symposium on
26-29 June 2005
Page(s):467
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476
Abstract:
We prove the finite homomorphism preservation theorem: a first-order formula is preserved under homomorphisms on finite structures iff it is equivalent in the finite to an existential positive formula. We also strengthen the classical homomorphism preservation theorem by showing that a formula is preserved under homomorphisms on all structures iff it is equivalent to an existential positive formula of the same quantifier rank. Our method involves analysis of existential positive types and a new notion of existential positive saturation.
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IEEE Conference
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IEE Conference
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