On Hausdorff limits of images of o-minimal families in real tori

25.05.2023 15:00 - 15:50

S. Starchenko (U of Notre Dame, US)

Let \(\{X_s \colon x\in S\}\) be a family of subsets of \({\mathbb R}^n\) definable in some o-minimal expansion of the real field.

Let \(\Gamma \subseteq {\mathbb R}^n\) be a lattice and \(\pi \colon {\mathbb R}^n/\Gamma \to \mathbb T\) be the quotient map.

In a series of papers (published and unpublished) together with Y. Peterzil we considered Hausdorff limits of the family \(\{ \pi(X_s)\colon s\in S\}\) and provided their description.

In this talk I describe model theoretic tools used in the description.




HS 11, 2. OG, OMP 1