Henselianity and the language of rings

Anscombe, S and Jahnke, F (2015) Henselianity and the language of rings. Arxiv.org .

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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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