Logic Seminar - Jorge Julián Prieto Jara - "Differentially closed fields and quasiminimality"

Wed, 21/03/201811:00-13:00
Ross 63

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.