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 :

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

**(eh)** is *elementarily henselian*, i.e. every is henselian,

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

**(-def) ** admits a -definable nontrivial henselian valuation.

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