The surreal numbers as a universal H-field
Logic
2016-08-12 v3 Classical Analysis and ODEs
Rings and Algebras
Abstract
We show that the natural embedding of the differential field of transseries into Conway's field of surreal numbers with the Berarducci-Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci-Mantova derivation.
Cite
@article{arxiv.1512.02267,
title = {The surreal numbers as a universal H-field},
author = {Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven},
journal= {arXiv preprint arXiv:1512.02267},
year = {2016}
}
Comments
18 pp; updated according to suggestions by the reviewer; to appear in J. Eur. Math. Soc. (JEMS)