Résume | Recently, Aschenbrenner, van den Dries, and van der Hoeven showed that all maximal Hardy fields have the same first-order theory as the field of LE-transseries (as differential fields). As a consequence, they deduce a transfer theorem for algebraic ODEs. I will discuss a strategy for extending this result to ODEs definable in an o-minimal expansion of the real field, and some partial progress in this direction. This talk is closely related to, but not dependent on, my November 4 talk in the Séminaire Général de Logique. |