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Abstract:

We investigate the question which henselian valuation rings are (externally) definable in the language of rings on a field K. The situation is very different depending on whether the residue field is algebraically closed or not. The main tool involved is the definability of the canonical p-henselian valuations (J.-Koenigsmann '15). In residue characteristic 0, our question has a satisfying answer - in positive characteristic, many open questions remain. (Work in progress)

Externally Definable Henselian Valuation Rings