| Résume | We study the complexity of the isomorphism relation for countable Archimedean groups, both in terms of Borel reducibility and with respect to the theory of potential classes developed by Hjorth, Kechris and Louveau. This will lead to a number of anti-classification results for such groups. We will also present similar results concerning the bi-embeddability relation over countable Archimedean groups and, if time permits, we will speak about analogous problems for countable models of certain o-minimal theories (ordered divisible abelian groups, real closed fields).
Joint work with F. Calderoni, D. Marker, and A. Shani. |
