arXiv subjects

Martina Liccardo

Publications and source records attributed to Martina Liccardo.

2 recordsLinked to original sources

arXiv2026

Stably Embedded Pairs of Ordered Abelian Groups

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 $\prod_{i\in ω} \mathbb{Z}$ are definable.

math.LO↗

arXiv2021

Ordered abelian groups that do not have elimination of imaginaries

We investigate the property of elimination of imaginaries for some special cases of ordered abelian groups. We show that certain Hahn products of ordered abelian groups do not eliminate imaginaries in the pure language of ordered groups. Moreover, we prove that, adding finitely many constants to the language of ordered abelian groups, the theories of the finite lexicographic products $\mathbb{Z}^n$ and $\mathbb{Z}^n \times \mathbb{Q}$ have definable Skolem functions.

math.LO↗