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Article Dans Une Revue Proceedings of the Edinburgh Mathematical Society Année : 2022

Revisiting closed asymptotic couples

Résumé

Abstract Every discrete definable subset of a closed asymptotic couple with ordered scalar field ${\boldsymbol {k}}$ is shown to be contained in a finite-dimensional ${\boldsymbol {k}}$ -linear subspace of that couple. It follows that the differential-valued field $\mathbb {T}$ 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 $\mathbb {R}$ as the underlying set for the second sort.
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Dates et versions

hal-03780802 , version 1 (19-11-2023)

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Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven. Revisiting closed asymptotic couples. Proceedings of the Edinburgh Mathematical Society, 2022, 65 (2), pp.530-555. ⟨10.1017/S0013091522000219⟩. ⟨hal-03780802⟩
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