Submission date: 5 October 2021

Abstract:

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:

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Full text arXiv 2110.02107: pdf, ps.