Theorem extension on short asymptotic couples reveals isomorphism to analytic hardy fields.
Differentially algebraic Hardy field extensions of short Hardy fields are short. This is proved in the more general setting of H-fields. As an application we extend a theorem of Rosenlicht (1981) by showing that each short asymptotic couple of Hardy type with small derivation is isomorphic to the asymptotic couple of an analytic Hardy field.
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Aschenbrenner et al. (2025) studied this question.
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