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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 19 mai 2017, 14h15

Lieu : Salle W, ENS

Tame Expansions of o-minimal Structures

Ayhan Günaydin (Bogazici)

Expanding 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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