The surreal numbers as a universal H-field

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.

18 pp; updated according to suggestions by the reviewer; to appear in J. Eur. Math. Soc. (JEMS)