The model theory of Cohen rings
Confluentes Mathematici, Tome 14 (2022) no. 2, pp. 1-28.

The aim of this article is to give a self-contained account of the algebra and model theory of Cohen rings, a natural generalization of Witt rings. Witt rings are only valuation rings in case the residue field is perfect, and Cohen rings arise as the Witt ring analogon over imperfect residue fields. Just as one studies truncated Witt rings to understand Witt rings, we study Cohen rings of positive characteristic as well as of characteristic zero. Our main results are a relative completeness and a relative model completeness result for Cohen rings, which imply the corresponding Ax-Kochen/Ershov type results for unramified henselian valued fields also in case the residue field is imperfect.

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DOI : 10.5802/cml.84
Classification : 03C60, 12L12, 13H05
Mots clés : model theory, henselian valued fields, Cohen rings, Ax-Kochen-Ershov

Sylvy Anscombe 1 ; Franziska Jahnke 2

1 Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013 Paris, France
2 Institut für Mathematische Logik und Grundlagenforschung, University of Münster, Einsteinstr. 62, 48149 Münster, Germany
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Sylvy Anscombe; Franziska Jahnke. The model theory of Cohen rings. Confluentes Mathematici, Tome 14 (2022) no. 2, pp. 1-28. doi : 10.5802/cml.84. https://cml.centre-mersenne.org/articles/10.5802/cml.84/

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