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Surreal numbers, derivations and transseries

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arxiv 1503.00315 v3 pith:6FFPWBSE submitted 2015-03-01 math.LO

Alessandro Berarducci , Vincenzo Mantova This is my paper · ORCID
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keywords numberssurrealdifferentialfieldstructuretransseriesadmitsauthors
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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, namely the derivation is surjective.

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  1. On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory

    math.LO 2025-01 conditional novelty 3.0 of 10

    Surreal numbers can be presented as sets of ordinals with a maximal 'birthday' element, giving a set-theoretic foundation equivalent to Gonshor's sign expansions and Conway's games.

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