vix.ing · top · new · best · stats · spec

Stably Embedded Pairs of Ordered Abelian Groups

2023/08/19 by Hils, Martin, Liccardo, Martina, Touchard, Pierre
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2308.09989

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 ∏i∈ ω ℤ are definable.

Related