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

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

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

Résumé

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.

langue originale	Anglais
Pages (de - à)	279-310
Nombre de pages	32
journal	Notre Dame Journal of Formal Logic
Volume	54
Numéro de publication	3-4
Les DOIs	https://doi.org/10.1215/00294527-2143898
état	Publié - 10 oct. 2013

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10.1215/00294527-2143898

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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.",

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AU - Aschenbrenner, Matthias

AU - Van Den Dries, Lou

AU - Van Der Hoeven, Joris

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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

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ER -

Toward a model theory for transseries

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