Submission date: 22 August 2020

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.

Mathematics Subject Classification: Primary 03C45, 03C60, Secondary 12L12, 12J25

Keywords and phrases:

Full text arXiv 2008.09889: pdf, ps.