EnglishFrançais

Site Web DMA

Bannière DMA Site de l'ENS Site Paris Sciences et Lettres Site du CNRS Accueil

Théorie des Modèles et Groupes

Horaires : Le mardi 24 septembre 2019, 16h - 17h30

Lieu : Sophie Germain, Salle 2015

H-structures

Alex Berenstein (Los Andes)

A complete theory T is called geometric if the algebraic closure has the exchange property in all models of T and the theory eliminates the quantifier exists infinity. In such theories there is a rudimentary notion of independence given by algebraic independence. Examples of geometric theories include SU-rank one theories and dense o-minimal theories. An expansion of a model M of T by a unary predicate H is called dense-codense if for every finite dimensional subset A of M and every non algebraic type p(x) over A, there is a realization of p(x) in H(M) and another one which is not algebraic over AH(M). A dense-codense expansion is called an H-structure if in addition H(M) is algebraically independent. In this talk we will talk about the basic properties of H-structures and how the new structure can be understood as a tame expansion of the original structure M. We will discuss groups definable in this expansion. We will also present some recent results on the special case when M is the ultrapower of a one-dimensional asymptotic class. This talk includes joint work with E. Vassiliev and D. Garcia and T. Zou.

 

Autres séances du séminaire


45 rue d'Ulm - F 75230 PARIS cedex 05 | phone : (33) 1 44 32 20 49 | fax : (33) 1 44 32 20 69

Plan du site | Mentions légales | | Edition du site | Web site designed under SPIP