Mariana VICARIA (Universität Münster) will give a talk on
An Imaginary Ax-Kochen Ershov principle
Abstract:
One of the most striking results of the model theory of henselian valued fields is the Ax-Kochen/Ershov principle, which roughly states that the first order theory of a henselian valued field that is unramified is completely determined by the first order theory of its residue field and the first order theory of its value group.
Our leading question is: Can one obtain an Imaginary Ax-Kochen/Ershov principle?
In previous work, I showed that the complexity of the value group requires adding the stabilizer sorts. In previous work, Hils and Rideau-Kikuchi showed that the complexity of the residue field reflects by adding the interpretable sets of the linear sorts. In this talk we present recent results on weak elimination of imaginaries that combine both strategies for a large class of (almost all) henselian valued fields of equicharacteristic zero.
This is joint work with Rideau-Kikuchi.