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Definable valuations induced by multiplicative subgroups and NIP fields

  • Katharina Dupont
  • Assaf HassonEmail author
  • Salma Kuhlmann
Article
  • 3 Downloads

Abstract

We study the algebraic implications of the non-independence property and variants thereof (dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a (definable) henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” (J Math Log 18(2):1850007, 2018).

Keywords

NIP Strong NIP Definable valuations Henselian fields Hahn series dp-minimal fields 

Mathematics Subject Classification

03C68 

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Notes

Acknowledgements

We would like to thank I. Efrat, M. Hils, F. Jahnke, M. Kamensky, F.-V. Kuhlmann and P. Simon for several ideas, corrections and suggestions.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.FB Mathematik und StatistikUniversität KonstanzConstanceGermany
  2. 2.Department of mathematicsBen Gurion University of the NegevBeershebaIsrael

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