Definability questions for o-minimal expansions of the real field
Presentations
Overview
Overview
abstract
In a series of papers on the expansion of the real field by all restricted analytic functions and the exponential function, Van den Dries, Macintyre and Marker pioneered a method for deciding whether a given function is definable or not in this structure. Their arguments are based on an embedding theorem of the Hardy field of definable univariate germs into the field of transseries. In collaboration with Rolin and Servi, we obtain such an embedding theorem for the expansion of the real field by any generalized quasianalytic class and the exponential function. This helps us decide, for instance, the non-definability of Gamma in the expansion of the real field by Zeta, and vice-versa. Other types of definability, such as the definability of the complex Gamma function on suitable domains, have also recently become of interest. I will give an overview of what we know (joint work with Padgett) and what we are currently working on (joint project with Binyamini).
