The number of countable differentially closed fields (Q998141)

The goal of this tutorial is to outline the Hrushovski-Sokolović proof of Vaught's Conjecture for differentially closed fields. The method of coding graphs into structures with ENI-DOP (developed by Shelah) is used for showing that there are continuum many countable differentially closed fields. Section 2 of the paper describes this method in some simple cases. The review of the model theory of differentially closed fields is done in Sections 3 and 4 and the core of the proof of Vaught's Conjecture is contained in Section 5 with general results illustrated before.