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

Voir la notice de l'article provenant de la source EMS Press

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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     title = {Surreal numbers, derivations and transseries},
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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. http://geodesic.mathdoc.fr/articles/10.4171/jems/769/

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