| Résume | Motivated by connections with questions from model theory of valued fields, we investigate problems of geometric nature in the model theory of divisible ordered Abelian groups (DOAG). We are particularly interested in finding algebraic characterizations of a model-theoretic independence relation, called non-forking independence. There was in previous literature an unsuccessful attempt to find such characterizations in DOAG, using standard techniques from o-minimal theory. We carried out a lower-level study of the geometric properties of ordered Abelian groups, and we found “invariants” which give us more control on types than what o-minimality allows, in particular we did compute forking in DOAG.
In this talk, we will present the geometric aspects of our work, describe those invariants, and explain the connections to forking. |
