When does dependence transfer from fields to henselian expansions?

Franziska Jahnke (M√ľnster)

Frank Adams 1,

Let K be an NIP field and let v be a henselian valuation on K. 
We ask whether (K,v) is NIP as a valued field. By a result of Shelah, we 
know that if v is externally definable, then (K,v) is NIP.

Using the definability of the canonical p-henselian valuation, we show 
that whenever the residue field of v is not separably closed, then v is 
externally definable.

We also discuss the case of separably closed residue fields.
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