A core question in the model theory of fields is to understand how combinatorial patterns and algebraic properties interact. The study of NIPn fields, which can’t express the edge relation of random n-hypergraph, is linked to henselianity. In this talk, we use Chernikov and Hils conditions to obtain transfer in some situations, that is, under some algebraic assumptions, it is enough to know that the residue field of a henselian valued field is NIPn in order to known that it is itself NIPn, and we discuss consequences on hypothetical strictly NIPn fields.
- Théorie des Modèles et Groupes