JournalsjemsVol. 21, No. 4pp. 1179–1199

The surreal numbers as a universal -field

  • Matthias Aschenbrenner

    University of California Los Angeles, USA

  • Lou van den Dries

    University of Illinois at Urbana-Champaign, Urbana, USA

  • Joris van der Hoeven

    Ecole Polytechnique, Palaiseau, France
The surreal numbers as a universal $H$-field cover
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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 this article

Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven, The surreal numbers as a universal -field. J. Eur. Math. Soc. 21 (2019), no. 4, pp. 1179–1199

DOI 10.4171/JEMS/858