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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 19 mai 2017, 11h

Lieu : Salle W, ENS

Beyond o-minimality, and why

Chris Miller (Ohio State)

O-minimal structures on the real field have many desirable properties. As examples: (a) Hausdorff (and even packing) dimension agrees with topological dimension on locally closed definable sets. (b) Locally closed definable sets have few rational points (in the sense of the Pila-Wilkie Theorem). (c) For each positive integer p, every closed definable set is the zero set of a definable C^p function. (d) Connected components of definable sets are definable. But to what extent is o-minimality necessary for these properties to hold? I will discuss this question, and illustrate via examples as to why one might care about answers.


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