Pietro Freni (University of Leeds) – Cuts and derivations in exponential o-minimal fields

Abstract: After a brief historical survey I will describe how some axioms of the theory of Hardy fields can be generalized so as to cover the case of differential fields of germs at a non-principal cut in an o-minimal ordered field. I will sketch how this can be used to prove that Tressl's signature alternative holds in a large class of exponential o-minimal theories.