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The surreal numbers as a universal -field
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
Source 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.
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