%0 Journal Article
%T Surreal numbers, derivations and transseries
%A Alessandro Berarducci
%A Vincenzo Mantova
%J Mathematics
%D 2015
%I arXiv
%X Several authors have conjectured that Conway's field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy-type. In this paper we give a complete positive solution to both problems. We also show that with this new differential structure, the surreal numbers are Liouville closed, namely the derivation is surjective.
%U http://arxiv.org/abs/1503.00315v3