arXiv:1503.00315 Abstract | arXiv Analytics

arXiv:1503.00315 [math.LO]Abstract References Reviews Resources

Surreal numbers, derivations and transseries

Published 2015-03-01Version 1

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.

Comments: 46 pages

Categories: math.LO

Subjects: 03C64, 16W60, 04A10, 26A12, 13N15

Keywords: surreal numbers, transseries, derivation, exponential function, compatible differential structure

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