Stably Embedded Pairs of Ordered Abelian Groups [Stabil eingebettete Paare angeordneter abelscher Gruppen]

Hils, Martin; Liccardo, Martina; Touchard, Pierre

Zusammenfassung

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 ∏[i∈ω] Z are definable.