Dp-minimal valued fields

Pierre Simon (1) , Jahnke Franziska , Walsberg Erik

1 AGL - Algèbre, géométrie, logique

We show that dp-minimal valued fields are henselian and that a dp-minimal field admitting a definable type V topology is either real closed, algebraically closed or admits a non-trivial definable henselian valuation. We give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.

Mots clés: NIP; vauled fields; dp-minimal

Domaines: Logique [math.LO]

Pierre Simon, Jahnke Franziska, Walsberg Erik. Dp-minimal valued fields. 2015. ⟨hal-01183357⟩