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Definable henselian valuations in positive residue characteristic
Published 12 Jan 2024 in math.LO and math.AC | (2401.06884v2)
Abstract: We study the question of $\mathcal{L}_{\mathrm{ring}}$-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.
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