Submission date: 21 November 2012.

Abstract:

On a Henselian valued field (K,V) where V is the valuation ring, if the value group contains a convex p-regular subgroup which is not p-divisible, then V is definable in the language of rings. A Henselian valuation ring with a regular non-divisible value group is always 0-definable. In particular, some results of Ax's and Konenigmann's are generalized.

Mathematics Subject Classification: 03C30, 03C40, 03C60

Keywords and phrases: definable valuations, henselian valued fields, non-divisible groups, regular ordered abelian groups

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