O-minimal residue fields of o-minimal fields

摘要

Let R be an o-minimal field with a proper convex subring V. We axiomatize the class of all structures (R,V) such that kind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in Ma?íková (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.