Surreal numbers, derivations and transseries

Abstract

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.

47 pages; minor corrections and typographical improvements

Cited by in corpus (5)

• Transseries as germs of surreal functions
• Generic derivations on o-minimal structures
• Exponential fields and Conway's omega-map
• Relative differential closure in Hardy fields
• On Vector Spaces with Formal Infinite Sums