Definable non-divisible Henselian valuations
Abstract
On a Henselian valued field ( K , V ), where V is the valuation ring, if the value group contains a convex p -regular subgroup that 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 and of Konenigmann are generalized.