The surreal numbers as a universal -field
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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.

Authors: Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven

Keywords: surreal numbers, derivation, H-fields, fields of transseries

A.M.S. subject classification: 03C64, 16W60, 12H05, 26A12, 26E30

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