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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.more » « less
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Aschenbrenner, Matthias ; van den Dries, Lou ; van der Hoeven, Joris ( , Revista de la Unión Matemática Argentina)
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Aschenbrenner, Matthias ; van den Dries, Lou ; van der Hoeven, Joris ( , Journal of the European Mathematical Society)
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Aschenbrenner, Matthias ; van den Dries, Lou ; van der Hoeven, Joris ( , Proceedings of the London Mathematical Society)