Definable valuations induced by multiplicative subgroups and NIP fields

Katharina Dupont; Assaf Hasson; Salma Kuhlmann

doi:https://doi.org/10.1007/s00153-019-00661-2

Definable valuations induced by multiplicative subgroups and NIP fields

Katharina Dupont, Assaf Hasson, Salma Kuhlmann

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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 language	American English
Pages (from-to)	819-839
Number of pages	21
Journal	Archive for Mathematical Logic
Volume	58
Issue number	7-8
DOIs	https://doi.org/10.1007/s00153-019-00661-2
State	Published - 1 Nov 2019

Keywords

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

All Science Journal Classification (ASJC) codes

Philosophy
Logic

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Cite this

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keywords = "Definable valuations, Hahn series, Henselian fields, NIP, Strong NIP, dp-minimal fields",

author = "Katharina Dupont and Assaf Hasson and Salma Kuhlmann",

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AU - Hasson, Assaf

AU - Kuhlmann, Salma

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N2 - 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).

AB - 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).

KW - Definable valuations

KW - Hahn series

KW - Henselian fields

KW - NIP

KW - Strong NIP

KW - dp-minimal fields

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JO - Archive for Mathematical Logic

JF - Archive for Mathematical Logic

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ER -

Definable valuations induced by multiplicative subgroups and NIP fields

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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