Séminaire Logique mathématique ICJ

Definable topological dynamics and o-minimality

par Grzegorz Jagiella

Europe/Paris
112 (ICJ, bât. Braconnier, UCBL - La Doua)

112

ICJ, bât. Braconnier, UCBL - La Doua

Description

In definable topological dynamics we consider model-theoretic analogues of classic dynamical objects. For a fixed structure M we consider a definable group G and the category of definable flows over M. We then consider (classic) objects associated with a given definable flow, such as minimal flows or the Ellis group of the universal definable flow over M. Results by Newelski, Pillay and Krupiński show a highly model-theoretic nature of these objects. This raises questions about the relationships between such objects calculated over M with their counterparts calculated in an elementary extension N of M. In the talk I will say about results and the standing conjecture about Ellis groups of universal definable flows. I will also describe how we prove a strong version of the conjecture for o-minimal expansions of real closed fields, by means of explicit description of the Ellis group in model-theoretic terms.