Small sets in dense pairs

par Panteleimon Eleftheriou (Universität Konstanz)

jeudi 6 avr. 2017, 16:15 → 17:15 Europe/Paris

Salle de séminaire 1 sous-sol (ICJ, bât. Braconnier, UCBL - La Doua)

Let (M, P) be an expansion of an o-minimal structure M by a dense set P, such that two tameness conditions hold. We prove that every P-bound set X, definable in (M, P), can be definably embedded into some cartesian power of P, uniformly in parameters. The proof goes through an elimination of imaginaries result for the structure induced on P by M. We verify the tameness conditions in examples, such as dense pairs, Mann pairs and expansions of M by dense independent sets.