Abstract:

We will introduce different types of bi-interpretations and show how to apply them to algebraic and model-theoretic problems of Chevalley groups over fields. For example: 1. We will show that any group elementary equivalent to some Chevalley group is a Chevalley group itself. 2. We will show that the Diophantine problem in any Chevalley group over a ring R is equivalent to the Diophantine problem of R.