Venue
Sala Seminari (Dip. Matematica).
Abstract
Il seminario è stato cancellato. Sarà riprogrammato in altra data. Alessandro Berarducci P. Eleftheriou, “Characterizing o-minimal groups in tame expansions of o-minimal structures”, Journal of the Institute of Mathematics of Jussieu, Online first (2019), 1-26.Let N be an expansion of an o-minimal structure M that admits a good dimension theory. Several NIP pairs N=(M, P) fall under this category, such as when P is a dense elementary substructure of M, or it is a multiplicative Mann group, or a dense independent set. We prove: (1) a Weil’s group chunk theorem that guarantees a definable group with an o-minimal group chunk is o-minimal, (2) a full characterization of those definable groups that are o-minimal as those groups that have maximal dimension; namely, their dimension equals the dimension of their topological closure, (3) as an application, if N expands M by a dense independent set, then every definable group is o-minimal. P. Eleftheriou, “Characterizing o-minimal groups in tame expansions of o-minimal structures”, Journal of the Institute of Mathematics of Jussieu, Online first (2019), 1-26.