Toward a model theory for transseries

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

doi:10.1215/00294527-2143898

Toward a model theory for transseries

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

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

Abstract

The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

Original language	English
Pages (from-to)	279-310
Number of pages	32
Journal	Notre Dame Journal of Formal Logic
Volume	54
Issue number	3-4
DOIs	https://doi.org/10.1215/00294527-2143898
Publication status	Published - 10 Oct 2013

Keywords

Differential fields
Hardy fields
Model completeness
NIP
Transseries

Access to Document

10.1215/00294527-2143898

Cite this

@article{9d7f4250a4fd4739870b5d274ecd9199,

title = "Toward a model theory for transseries",

abstract = "The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.",

keywords = "Differential fields, Hardy fields, Model completeness, NIP, Transseries",

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

year = "2013",

month = oct,

day = "10",

doi = "10.1215/00294527-2143898",

language = "English",

volume = "54",

pages = "279--310",

journal = "Notre Dame Journal of Formal Logic",

issn = "0029-4527",

number = "3-4",

}

TY - JOUR

T1 - Toward a model theory for transseries

AU - Aschenbrenner, Matthias

AU - Van Den Dries, Lou

AU - Van Der Hoeven, Joris

PY - 2013/10/10

Y1 - 2013/10/10

N2 - The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

AB - The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

KW - Differential fields

KW - Hardy fields

KW - Model completeness

KW - NIP

KW - Transseries

UR - https://www.scopus.com/pages/publications/84885028034

U2 - 10.1215/00294527-2143898

DO - 10.1215/00294527-2143898

M3 - Article

AN - SCOPUS:84885028034

SN - 0029-4527

VL - 54

SP - 279

EP - 310

JO - Notre Dame Journal of Formal Logic

JF - Notre Dame Journal of Formal Logic

IS - 3-4

ER -

Toward a model theory for transseries

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this