On n-dependent groups and fields

Mathematical Logic Quarterly 62 (3):215-224 (2016)
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Abstract

First, an example of a 2-dependent group without a minimal subgroup of bounded index is given. Second, all infinite n-dependent fields are shown to be Artin-Schreier closed. Furthermore, the theory of any non separably closed PAC field has the IPn property for all natural numbers n and certain properties of dependent valued fields extend to the n-dependent context.

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10.1002/malq.201400080

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Citations of this work

Finite Undecidability in Nip Fields.Brian Tyrrell - forthcoming - Journal of Symbolic Logic:1-24.
On $n$ -Dependence.Artem Chernikov, Daniel Palacin & Kota Takeuchi - 2019 - Notre Dame Journal of Formal Logic 60 (2):195-214.
Distality Rank.Roland Walker - 2023 - Journal of Symbolic Logic 88 (2):704-737.

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References found in this work

Definable Henselian valuations.Franziska Jahnke & Jochen Koenigsmann - 2015 - Journal of Symbolic Logic 80 (1):85-99.
Corps et chirurgie.Anand Pillay & Bruno Poizat - 1995 - Journal of Symbolic Logic 60 (2):528-533.
Superstable fields and groups.G. Cherlin - 1980 - Annals of Mathematical Logic 18 (3):227.
Subgroups of the additive group of a separably closed field.Thomas Blossier - 2005 - Annals of Pure and Applied Logic 134 (2-3):169-216.

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