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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