Zilber introduced quasi-minimal classes to generalize the model theory of pseudo exponential fields. They are equipped with a pregeometry operator and satisfy interesting properties such as having only countable or co-countable definable sets. Differentially closed fields of characteristic 0, rich examples of a \omega-stable structures, are good candidates to be quasiminimal. The difficulty is that a differential equation may have uncountably many solutions, and thus violate the countable closure requirement of quasiminimal structures. Nonetheless, when a field is built sparingly enough, it does turn out to be quasi-minimal. In this talk we sketch a proof that: a differentially closed field is quasi-minimal iff it is prime over some set of independent coefficients.
Wed, 21/03/2018 - 11:00 to 13:00