Submission date: 12 January 2024

Abstract:

We study the question of ℒ_{ring}-definability of non-trivial henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we provide a characterization of henselian fields that admit a non-trivial definable henselian valuation. In particular, we treat cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields.

Mathematics Subject Classification: 03C60, 12L12

Keywords and phrases:

Full text arXiv 2401.06884: pdf, ps.