chapter  1
Pages 1

The notes are organized as follows. Section 1 gives some preliminary alge­ braic results and definitions (difference fields, varieties, Zariski topology, etc.). Section 2 introduces the theory ACFA of generic difference fields and proves elementary results about it. Section 3 introduces the notions of independence and SU-rank and shows various results about them. In Section 4 we study the fixed field, and in Section 5 the notions of orthogonality and modularity. Section 6 introduces generics and stabilizers of groups. Finally, Section 7 con­ tains some of the hard results in the area and the applications by Hrushovski to problems in number theory. At the end of the notes, you will find some references and “further reading” on difference fields, with comments.