Seminar

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

Given a complete theory T of henselian valued fields of characteristic 0, we  axiomatize the class of existentially closed differential expansions of models of T. Let us denote this axiomatization by T_\delta^*. Then we examine which model-theoretic properties transfer from T to T_\delta^* such as the existence of a dimension function on definable sets, or the existence of a code for definable sets (elimination of imaginaries). The main technical tool is a cell decomposition theorem for models of T and a description of definable functions (and more generally correspondences). (This is the analog in this setting of a result of P. Simon and E. Walsberg for dp-minimal, non strongly minimal fields of characteristic 0). Then we illustrate why this set-up is convenient to look at dense pairs of models of T. This is joint work with Nicolas Guzy and Pablo Cubidès.

Generic Differential Expansions Of Topological Fields Of Characteristic 0