Logic Seminar

Pantelis Eleftheriou, University of Konstanz

"Small sets in dense pairs"

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 can be definably embedded into some P^n, uniformly in parameters. We then 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.

MC 5403