Henselianity in the language of rings
classification
🧮 math.LO
keywords
characteristicconsiderdefinabledifferentelementarilyequicharacteristicequivalentexistence
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We consider four properties of a field $K$ related to the existence of (definable) henselian valuations on $K$ and on elementarily equivalent fields, and study the implications between them. Surprisingly, the full pictures look very different in equicharacteristic and mixed characteristic.
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