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

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

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1179-1199
Number of pages	21
Journal	Journal of the European Mathematical Society
Volume	21
Issue number	4
DOIs	https://doi.org/10.4171/JEMS/858
Publication status	Published - 1 Jan 2019

Keywords

Differential fields
Hardy fields
Surreal numbers
Transseries

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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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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

VL - 21

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

Abstract

Keywords

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