O-minimal residue fields of o-minimal fields

Let R be an o-minimal field with a proper convex subring V . We axiomatize the class of all structures ( R , V ) such that k ind , the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in Maříková (2010) [8] it was shown that certain first-order conditions on ( R , V ) are sufficient for the o-minimality of k ind . Here we prove that these conditions are also necessary.