Stably Embedded Pairs of Ordered Abelian Groups

Abstract

We investigate when an ordered abelian group $G$ is stably embedded in a given elementary extension $H$. We focus on a large class of ordered groups which includes maximal ordered groups with interpretable archimedean valuation. We give a complete answer for groups in this class which takes the form of a transfer principle for valued groups. It follows in particular that all types in the lexicographic product ${\prod }_{i\in \ddot{I}‰}\mathbb{Z}$ are definable.

45 pages