Restrained structures
Restrained structures
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)