Revisiting closed asymptotic couples

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

Research output: Contribution to journalArticlepeer-review


Every discrete definable subset of a closed asymptotic couple with ordered scalar field k is shown to be contained in a finite-dimensional k-linear subspace of that couple. It follows that the differential-valued field T of transseries induces more structure on its value group than what is definable in its asymptotic couple equipped with its scalar multiplication by real numbers, where this asymptotic couple is construed as a two-sorted structure with ℝ as the underlying set for the second sort.

Original languageEnglish (US)
Pages (from-to)530-555
Number of pages26
JournalProceedings of the Edinburgh Mathematical Society
Issue number2
StatePublished - May 20 2022


  • Hardy fields
  • asymptotic couples
  • transseries

ASJC Scopus subject areas

  • General Mathematics


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