Towards a Model Theory for Transseries
  The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field, and report on our efforts to understand its first-order theory. 
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
math.LO math.DS