We investigate distality and existence of distal expansions in valued fields related structures. In particular, we characterize a large class ordered abelian groups, provide an Ax-Kochen-Eršov-style characterization for henselian fields, demonstrate that certain e.g., the differential field logarithmic-exponential transseries, are distal. As new tool analyzing employ relative quantifier elimina...

We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.