Abstract: 

In this talk we present a work in progress, joint with Junguk Lee, on pairs ofstructures. We focus first on fields and, time permitting, discuss a broader setting. Delon proved Q.E. in pairs of ACF in a language

expanded by functions for the coefficients oflinear dependence relations over the distinguished subfield P. More recently, using this language, D'Elbee, Kaplan and Neuhauser have shown Q.E. and classification results in the broader context where P is a field equipped with additional structure inside a model of ACF. We will go through their work and present a few results that generalizes it by replacing the ambient algebraically closed field by a model of a stable theory T_(0) extending the theory of fields in a language L_{0} and satisfying a few conditions,and P by an L_{0}-substructure with additionalstructure. We highlight the differences that appear in the proofs with the case of ACF.

Zoom:717 463 6082