DEFINABLE HENSELIAN VALUATIONS IN POSITIVE RESIDUE CHARACTERISTIC

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 the cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields.