Definable valuations induced by multiplicative subgroups and NIP fields

Katharina Dupont, Assaf Hasson, Salma Kuhlmann

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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).

Original languageEnglish
Pages (from-to)819-839
Number of pages21
JournalArchive for Mathematical Logic
Volume58
Issue number7-8
DOIs
StatePublished - 1 Nov 2019

Keywords

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

ASJC Scopus subject areas

  • Philosophy
  • Logic

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