| Résume | Interest in transseries and Hardy fields comes from several fields, including asymptotic analysis, dynamical systems, and model theory of the real numbers. The first-order theory of (logarithmic-exponential) transseries and maximal Hardy fields is completely axiomatized by the theory of closed H-fields, which is model complete, as Aschenbrenner, van den Dries, and van der Hoeven have shown in a long series of works. I will describe my extension of this model completeness to tame pairs of closed H-fields, in order to better understand large closed H-fields, such as maximal Hardy fields, hyperseries, or surreal numbers. Time permitting, I may mention ongoing work on differential-algebraic dimension in transserial tame pairs or at least some of its consequences. |
