Toward a model theory for transseries

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)279-310
Number of pages32
JournalNotre Dame Journal of Formal Logic
Volume54
Issue number3-4
DOIs
StatePublished - Oct 10 2013

Fingerprint

Model Theory
O-minimal Structures
Laurent Series
Asymptotic Expansion
Vector Field
Model

Keywords

  • Differential fields
  • Hardy fields
  • Model completeness
  • NIP
  • Transseries

ASJC Scopus subject areas

  • Logic

Cite this

Toward a model theory for transseries. / Aschenbrenner, Matthias; Van Den Dries, Lou; Van Der Hoeven, Joris.

In: Notre Dame Journal of Formal Logic, Vol. 54, No. 3-4, 10.10.2013, p. 279-310.

Research output: Contribution to journalArticle

Aschenbrenner, Matthias ; Van Den Dries, Lou ; Van Der Hoeven, Joris. / Toward a model theory for transseries. In: Notre Dame Journal of Formal Logic. 2013 ; Vol. 54, No. 3-4. pp. 279-310.
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