Speaker
Anna Dmitrieva
University of East Anglia
Talks at this conference:
Monday, 14:40, J330 
Generic functions and quasiminimality 
In 2002 Zilber introduced the theory of a generic function on a field [4], coinciding with the limit theory of generic polynomials from [2]. Axiomatized in firstorder logic by a version of Schanuel property and existential closedness, this theory turns out to be ωstable. As shown by Wilkie [3] and Koiran [1], one can explicitly construct such a generic function on the complex plane in a form of a Taylor series, using the ideas behind Liouville numbers. In this talk we look further into the properties of the theory of generic functions. As the main result, we show that adding any of these generic functions to the complex field gives an isomorphic structure, which ought to be quasiminimal, i.e. any definable subset has to be countable or cocountable. Thus we obtain a nontrivial example of an entire function which keeps the complex field quasiminimal. Bibliography
