Interpretability of Galois groups of first order structures

Let $T$ be a complete theory with uniform EI and QE in a language $L$. Let $\mathfrak{C}$ be a monster model of $T$ and let $K$ be a small substructure of $\mathfrak{C}$. We show that the sorted complete system of Galois group of $K$ is uniformly interpretable in the $L_P$-structure $(M,K)$ for any elementary substructure of $\mathfrak{C}$ containing $K$, where the language $L_P$ is an expansion of $L$ by adding a new unary predicate $P$. Using this interpretability result, we give a description of types in PAC structures in terms of sorted complete systems. This is a joint work with Daniel M. Hoffmann.