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Preprint Number 1541

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1541. Pantelis E. Eleftheriou
Small sets in Mann pairs

Submission date: 19 December 2018


Let M˜= < M, G > be an expansion of a real closed field M by a dense subgroup G of < M^{>0}, × > with the Mann property. We prove that the induced structure on G by M eliminates imaginaries. As a consequence, every small set X definable in M can be definably embedded into some G^l, uniformly in parameters. These results are proved in a more general setting, where M ˜ = < M, P > is an expansion of an o-minimal structure M by a dense set P ⊆ M, satisfying three tameness conditions.

Mathematics Subject Classification: 03C64

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Full text arXiv 1812.07970: pdf, ps.

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