When Does Nip Transfer from Fields to Henselian Expansions?
نویسنده
چکیده
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 give a weaker statement for the case of separably closed residue fields.
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