Appears in collection : 2018 - T1 - WS2 - Model theory and valued fields

For first order structures on real closed fields, a very simple condition, namely o-minimality, implies strong tameness results about definable sets. In this talk, I will present an analogue of this in valued fields, which encompasses most settings in which definable sets are known to behave tamely. In contrast, previously known analogues were either restricted to certain subclasses of valued fields (like P-minimality, C-minimality, v-minimality) or simply imposed almost all things one would like to have as axioms (b-minimality with centers and the Jacobian property). This is joint work with Cluckers and Rideau.