Henselianity in the language of rings, with Franziska Jahnke

I would like to write about a new paper ([AJ15]) which Franziska Jahnke and I have written and put on the arXiv. It’s called Henselianity in the language of rings. In it we investigate the relationship between the following four properties of a field K:

(h) K is henselian, i.e. K admits a nontrivial henselian valuation,

(eh) K is elementarily henselian, i.e. every L\equiv K is henselian,

(def) K admits a definable nontrivial henselian valuation, and

(\emptyset-def) K admits a \emptyset-definable nontrivial henselian valuation.

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