Recent Progress on Definability of Henselian Valuations
  Although the study of the definability of henselian valuations has a long history starting with J. Robinson, most of the results in this area were proven during the last few years. We survey these results which address the definability of concrete henselian valuations, the existence of definable henselian valuations on a given field, and questions of uniformity and quantifier complexity. 
Arno Fehm and Franziska Jahnke
math.LO