Submission date: 19 December 2018

Abstract:

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

Keywords and phrases:

Full text arXiv 1812.07970: pdf, ps.