Every discrete definable subset of a closed asymptotic couple with ordered scalar field is shown to be contained in a finite-dimensional -linear subspace of that couple. It follows that the differential-valued field 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 as the underlying set for the second sort.

Authors: Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven

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