| Résume | Shelah's Conjecture states that any infinite field without the independence property (NIP) has to admit a non-trivial henselian valuation, unless it is separably closed or real closed. This conjecture was proved by Johnson for the class of fields of finite dp-rank, a subclass of NIP fields. In this talk I will present the general strategy used in Johnson's work to study fields of finite dp-rank, going through some of the equivalent and weaker conjectures regarding existence and uniqueness of definable V-topologies in such fields. |
