Séminaires : Géométrie et Théorie des Modèles

Equipe(s) : lm,
Responsables :Zoé Chatzidakis, Raf Cluckers, Georges Comte
Email des responsables : zoe.chatzidakis@imj-prg.fr
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Pour recevoir le programme par e-mail, écrivez à : zoe.chatzidakis@imj-prg.fr
Pour les personnes ne connaissant pas du tout de théorie des modèles, des notes introduisant les notions de base (formules, ensembles définissables, théorème de compacité, etc.) sont disponibles ici : https://webusers.imj-prg.fr/~zoe.chatzidakis/papiers/MTluminy.dvi/MTluminy.dvi. Ces personnes peuvent aussi consulter les premiers chapitres du livre Model Theory and Algebraic Geometry, E. Bouscaren ed., Springer Verlag, Lecture Notes in Mathematics 1696, Berlin 1998.Retour ligne automatique
Les notes de quelques-uns des exposés sont disponibles.

Orateur(s) Ayhan Günaydin - Bogazici,
Titre Tame Expansions of o-minimal Structures
Date19/05/2017
Horaire14:15 à 15:45
Diffusion
RésumeExpanding a model theoretically “tame” structure in a way that it stays “tame” has been a theme in the recent years. In the first part of this talk, we present a history of work done in that frame. Then we focus on the case of expansions of o-minimal structures by a unary predicate. There is a dividing line according to whether the predicate is dense or discrete; even though the results obtained are similar, there is an enormous difference in the techniques used. We shall present some of the results obtained in the dense case. Starting from a set of abstract axioms, we obtain a decomposition theorem for definable sets and a local structure theorem for definable groups.
The abstract axioms mentioned above are “smallness”, “o-minimal open core” and “quantifier elimination up to existential formulas”. We shall illustrate a proof of the fact that the first two imply “quantifier elimination up to bounded formulas”, which is a weak form of the last axiom and we give reasons why it is really weaker than that axiom.
(Joint work with P. Eleftheriou and P. Hieronymi)
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