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Henselianity in the language of rings

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Anscombe, Sylvy ORCID: 0000-0002-9930-2804 and Jahnke, Franziska (2018) Henselianity in the language of rings. Annals of Pure and Applied Logic, 169 (9). pp. 872-895. ISSN 0168-0072

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Official URL: https://doi.org/10.1016/j.apal.2018.04.008

Abstract

We consider four properties of a field K related to the existence of (de-finable) henselian valuations on K and on elementarily equivalent fields and study the implications between them. Surprisingly, the full pictures look very different in equichar-
acteristic and mixed characteristic.

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