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Definable non-divisible Henselian valuations

Definable non-divisible Henselian valuations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

Definable non-divisible Henselian valuations

Definable non-divisible Henselian valuations

Bulletin of the London Mathematical Society , Volume 46 (1) – Feb 1, 2014

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.

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References (16)

Publisher
Oxford University Press
Copyright
© 2013 London Mathematical Society
Subject
PAPERS
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdt074
Publisher site
See Article on Publisher Site

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.

Journal

Bulletin of the London Mathematical SocietyOxford University Press

Published: Feb 1, 2014

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