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arXiv · 2008.09889

Distality in valued fields and related structures

Matthias Aschenbrenner·Artem Chernikov·Allen Gehret·Martin Ziegler
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Abstract

We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian valued fields, and demonstrate that certain expansions of fields, e.g., the differential field of logarithmic-exponential transseries, are distal. As a new tool for analyzing valued fields we employ a relative quantifier elimination for pure short exact sequences of abelian groups.

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Matthias Aschenbrenner, Artem Chernikov, Allen Gehret, Martin Ziegler. 2020-08-22. Distality in valued fields and related structures. https://arxiv.org/abs/2008.09889

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