Around Hrushovski's Stabilizer Theorem

par Jean-Cyrille Massicot (UCBL)

jeudi 9 févr. 2017, 16:15 → 17:15 Europe/Paris

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

A K-approximate subgroup is a subset X of G such that X^2 is contained in at most K translates of X. The Stabilizer Theorem constructs a subgroup H of the group generated by X, with H type-definable and of bounded index. This allows not only for classification resultst in the study of approximate subgroups, but also for explicit construction of an X^00. However, this construction uses an expansion L^* of the language L of approximates subgroups. We will show how to obtain a subgroup H which is L-type definable, using Udi's theorem together with a result of Schlichting about families of subgroup, in a model-theoretic version of Ben Yaacov and Wagner, and an old theorem of Beth on definability.