Ayhan Gunaydin (Bosphorus University): Tame Expansions of o-minimal Structures
Thursday, 12.07.2018 11:00 im Raum SR 1D
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)
Angelegt am 04.07.2018 von Martina Pfeifer
Geändert am 04.07.2018 von Martina Pfeifer
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