Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2068

Preprint Number 2068

Previous Next Preprint server

2068. Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven
Revisiting closed asymptotic couples

Submission date: 5 October 2021


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.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2110.02107: pdf, ps.

Last updated: October 21 2021 20:51 Please send your corrections to: