Submission date: 19 January 2015.

Abstract:

We study the question which henselian fields admit definable henselian valuations (with or without parameters). We show that every field which admits a henselian valuation with non-divisible value group admits a parameter-definable (non-trivial) henselian valuation. In equicharacteristic 0, we give a complete characterization of henselian fields admitting a parameter-definable (non-trivial) henselian valuation. We also obtain partial characterization results of fields admitting 0-definable (non-trivial) henselian valuations. We then draw some Galois-theoretic conclusions from our results.

Mathematics Subject Classification: 03C40, 12J10 (primary), 03C60, 12L12, 12E30, 13F30 (secondary)

Keywords and phrases:

Full text arXiv 1501.04506: pdf, ps.