 
Summary: Some Remarks About Asymptotic Couples
Matthias Aschenbrenner
Department of Mathematics
University of Illinois at UrbanaChampaign
Urbana, IL 61801, U.S.A.
Current address: Department of Mathematics
University of California at Berkeley
Berkeley, CA 94720, U.S.A.
maschenb@math.uiuc.edu
Abstract. Asymptotic couples (of Htype) 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 modeltheoretic 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 Htype, the VapnikChernovenkis
property for sets definable in closed asymptotic couples of Htype, and
the relation of asymptotic couples of Htype to the "contraction groups"
of [6].
Introduction
