Some Remarks About Asymptotic Couples

Asymptotic couples (of H-type) try to capture the structure induced by the derivation of a Hardy field K on the value group of the natural valuation on K. In this note we continue the study of algebraic and model-theoretic aspects of asymptotic couples undertaken in [1]. We give a short exposition of some basic facts about asymptotic couples, and address a few topics left out in that paper: the (non-) minimality of the “closure” of an asymptotic couple of H-type, the Vapnik-Chernovenkis property for sets definable in closed asymptotic couples of H-type, and the relation of asymptotic couples of H-type to the “contraction groups” of [6].