NIP henselian valued fields

Pierre Simon (1) , Jahnke Franziska

1 AGL - Algèbre, géométrie, logique

We show that any theory of tame henselian valued fields is NIP if and only if the theory of its residue field and the theory of its value group are NIP. Moreover, we show that if (K,v) is a henselian valued field of residue characteristic char(Kv)=p for which K×/(K×)p is finite in case p>0, then (K,v) is NIP iff Kv is NIP and v is roughly tame.

Domaines: Logique [math.LO]

Pierre Simon, Jahnke Franziska. NIP henselian valued fields. 2016. ⟨hal-01351192⟩