The surreal numbers as a universal H-field

Matthias Aschenbrenner; Lou Van Den Dries; Joris Van Der Hoeven

doi:10.4171/JEMS/858

The surreal numbers as a universal H-field

Matthias Aschenbrenner
, Lou Van Den Dries
, Joris Van Der Hoeven

Department of Mathematics
University of California, Los Angeles
Department of Mathematics
University of Illinois at Urbana-Champaign

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

10 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	1179-1199
Nombre de pages	21
journal	Journal of the European Mathematical Society
Volume	21
Numéro de publication	4
Les DOIs	https://doi.org/10.4171/JEMS/858
état	Publié - 1 janv. 2019

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10.4171/JEMS/858

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title = "The surreal numbers as a universal H-field",

abstract = "We show that the natural embedding of the differential field of transseries into Conway{\textquoteright}s field of surreal numbers with the Berarducci{\textendash}Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci{\textendash}Mantova derivation.",

keywords = "Differential fields, Hardy fields, Surreal numbers, Transseries",

author = "Matthias Aschenbrenner and \{Van Den Dries\}, Lou and \{Van Der Hoeven\}, Joris",

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year = "2019",

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doi = "10.4171/JEMS/858",

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T1 - The surreal numbers as a universal H-field

AU - Aschenbrenner, Matthias

AU - Van Den Dries, Lou

AU - Van Der Hoeven, Joris

N1 - Publisher Copyright: © European Mathematical Society 2019.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Differential fields

KW - Hardy fields

KW - Surreal numbers

KW - Transseries

U2 - 10.4171/JEMS/858

DO - 10.4171/JEMS/858

M3 - Article

AN - SCOPUS:85062495462

SN - 1435-9855

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SP - 1179

EP - 1199

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 4

ER -

The surreal numbers as a universal H-field

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