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Summary: Some Remarks About Asymptotic Couples
Matthias Aschenbrenner
Department of Mathematics
University of Illinois at Urbana-Champaign
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 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].
Introduction
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