Geodesic
Surreal numbers, derivations and transseries
Journal of the European Mathematical Society, Tome 20 (2018) no. 2, pp. 339-390

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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.
DOI : 10.4171/jems/769
Classification : 03-XX, 13-XX, 16-XX, 26-XX
Keywords: Surreal numbers, transseries, Hardy fields, differential fields 
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Alessandro Berarducci; Vincenzo Mantova. Surreal numbers, derivations and transseries. Journal of the European Mathematical Society, Tome 20 (2018) no. 2, pp. 339-390. doi: 10.4171/jems/769

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