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Geometry and Model Theory

Time: Friday, October 07, 2011, 11h - 12h30

Location: amphithéâtre Rataud

Restrained structures

Antongiulio Fornasiero (Muenster)

We study first-order expansions of the real field that are restrained, i.e. that do not define the set of natural numbers. Being restrained is equivalent to several other notions of tameness. In particular: in a restrained structure, all reasonable notions of dimension (topological, Hausdorff, Minkowski, ...) coincide for unary closed definable sets (we also have partial results for non-unary sets); moreover, any continuous definable function is differentiable almost everywhere. Similar results hold also in definably complete structures outside the real line. Joint work with P. Hieromymi and C. Miller.


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