Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1208

Preprint Number 1208

Previous Next Preprint server

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.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1704.05802: pdf, ps.

Last updated: March 23 2021 10:20 Please send your corrections to: