On Model Theory of Valued Vector Spaces

TL;DR

This paper explores the model-theoretic properties of valued vector spaces, establishing transfer principles that relate their complexity to that of their base field and value set, using lexicographic product structures.

Contribution

It introduces transfer principles for valued vector spaces, linking their model-theoretic burden to that of the base field and value set, extending the analogy with valued fields.

Findings

Transfer principles for valued vector spaces established

Formula for computing burden in terms of base field and value set

Application of lexicographic products in model theory

Abstract

In analogy to valued fields, we study model-theoretic properties of valued vector spaces with variable base field by proving transfer principles down to the skeleton and down to the value set and base field. For instance, we give a formula which computes its burden in terms of the burden of its base field and its value set. To do this, we study these transfer principles in the context of lexicographic products of structures.