Submission date: 19 August 2023

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.

Mathematics Subject Classification:

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Full text arXiv 2308.09989: pdf, ps.