Applied Model Theory
Chair: James Freitag
Talks in this session
14:00 
Vincent Bagayoko, Ordered groups of regular growth rates 
This talk will regard some firstorder properties of ordered groups of germs of functions that are definable in an ominimal structure. I will describe my progress toward finding a tame firstorder theory of some of these groups, and give some elements of valuation theory on these ordered groups. 

14:40 
Anna Dmitrieva, 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


15:20 
Adele Padgett, Ominimal definitions of the complex Gamma and Riemann Zeta functions 
In this talk, I will discuss joint work with P. Speissegger in which we prove that the \(\Gamma\) function and Riemann’s \(\zeta\) function are ominimal on certain unbounded complex domains. I will also discuss some applications of this result. 