Surreal numbers, derivations and transseries
Berarducci, A, Mantova, V · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · 2018
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, that is, the derivation is surjective.