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Preprint Number 840

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840. Alessandro Berarducci and Vincenzo Mantova
Surreal numbers, derivations and transseries

Submission date: 1 March 2015.


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.

Mathematics Subject Classification: 03C64 16W60 04A10 26A12 13N15

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Full text arXiv 1503.00315: pdf, ps.

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