Elimination of imaginaries and stable domination in multivalued fields

Abstract: The model theory of henselian valued fields has been a major topic of study during the last century. Remarkable work has been achieved by Haskell, Hrushovski and Macpherson to understand the model theory of algebraically closed valued fields (ACVF). In a sequence of seminal papers they proved that this theory eliminates imaginaries once the geometric sorts are added and they developed the notion of stable domination, which describes how types over maximally complete bases are controlled by the stable part of the structure.

I will explain how to extend these results to the broader class of henselian valued fields of equicharacteristic zero, residue field algebraically closed and poly- regular value group. This includes many interesting mathematical structures such as the Laurent Series over the Complex numbers, but more importantly extends the results to valued fields with finitely many definable convex subgroups.

commutative algebralogicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic