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

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

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 (US)
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
State	Published - 2019

Keywords

Differential fields
Hardy fields
Surreal numbers
Transseries

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Online availability

10.4171/JEMS/858

Library availability

Discover UIUC Full Text

Cite this

@article{180d727a260547db81f82fc2918d1f31,

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–Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci–Mantova derivation.",

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

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

note = "Publisher Copyright: {\textcopyright} European Mathematical Society 2019.",

year = "2019",

doi = "10.4171/JEMS/858",

language = "English (US)",

volume = "21",

pages = "1179--1199",

journal = "Journal of the European Mathematical Society",

issn = "1435-9855",

publisher = "European Mathematical Society Publishing House",

number = "4",

}

TY - JOUR

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

Y1 - 2019

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

UR - http://www.scopus.com/inward/record.url?scp=85062495462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062495462&partnerID=8YFLogxK

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

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this