Using ultraproducts, I will describe the spectrum of the profinite completion of the integers and of the finite adeles over the rationals.The final aim is to describe the structure sheaf of these structures.Joint work with Margarita Otero and Angus Macintyre.
Nous présenterons une preuve de la Propriété (T) de Kazhdan pour les groupes d'automorphismes de structures métriques aleph_0-catégoriques. Ceci généralise des résultats précédents de Bekka (pour le groupe unitaire) et de Evans et Tsankov (pour les groupes pro-oligomorphes), sans besoin de faire appel à des résultats de classification de représentations unitaires. En effet, l'argument est purement modèle-théorique et basé sur des principes de la stabilité locale.
There is a well-known analogy between the arithmetic of rational numbers and the theory of meromorphic functions over a normed field. It is a classical result of Julia Robinson that the first order theory of the field of rational numbers is undecidable, and one would expect such a result in the meromorphic setting. In this talk I'll give an outline of the proof of undecidability for rigid meromorphic functions in positive characteristic
A continuous theory T of bounded metric structures is said to be kappa-categorical if T has a unique model of density kappa. Work of Ben Yaacov and Shelah+Usvyatsov shows that Morley's Theorem holds in this context: if T has a countable signature and is kappa-categorical for some uncountable kappa, then T is kappa-categorical for all uncountable kappa. In classical (discrete) model theory, there are several characterizations of uncountable categoricity. For example, there is a structure theorem for uncountably categorical theories T, due to Baldwin+Lachlan: there is a strongly minimal set […]
