Surreal numbers, derivations and transseries
Logic
2018-02-21 v3
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.
Cite
@article{arxiv.1503.00315,
title = {Surreal numbers, derivations and transseries},
author = {Alessandro Berarducci and Vincenzo Mantova},
journal= {arXiv preprint arXiv:1503.00315},
year = {2018}
}
Comments
47 pages; minor corrections and typographical improvements