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Preprint Number 1208

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1208. Pantelis E. Eleftheriou
Small sets in dense pairs

Submission date: 20 April 2017


Let (M, P) be an expansion of an o-minimal structure M by a dense subset P of M, such that three tameness conditions hold. We prove that the induced structure on P by M eliminates imaginaries. As a corollary, we obtain that every small set X definable in (M, P) can be definably embedded into some P^n, uniformly in parameters. We verify the tameness conditions in three examples: dense pairs, expansions of M by a dense independent set, and expansions by a dense divisible multiplicative group with the Mann property.

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Full text arXiv 1704.05802: pdf, ps.

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