Model theory of ordered valued fields

A field can have both an ordering and a valuation in different ways, but the most interesting is the case when the relations interact so that the valuation ring is convex with respect to the ordering. In this case, an o-minimal ordered field becomes a weakly o-minimal convexly valued field. In joint work with Ealy and Marikova we have shown that the convexly valued ordered ield is dominated by its residue field over its value group. Our next goal is to show that this result also holds for a T-convex theory. A longterm goal is to develop a theory of ordered Berkovich space.