Closed asymptotic couples
type: Item
instance of: scholarly article
title: Closed asymptotic couples
zbMATH Open document ID: 0974.12015
author: Matthias Aschenbrenner
author: Lou van den Dries
published in: Journal of Algebra
publication date: 2000-08-13T00:00:00Z
review text: The authors investigate asymptotic couples of Hardy type in the sense of \textit{M. Rosenlicht} [Am. J. Math. 103, 977-996 (1981; Zbl 0474.12020)]. The asymptotic couples with scalar multiplication associated to Hardy fields \(F\) belong to a certain elementary class, the class of H-couples. If \(F\) is a maximal Hardy field, its associated H-couple is closed (The authors give precise definitions in Section 1 of the paper.) The main result is that closed H-couples have an elimination theory. \textit{L. van den Dries, A. J. Macintyre} and \textit{D. E. Marker} in one of the most influential papers in model theory of the 1990s [Ann. Math. (2) 140, No. 1, 183-205 (1994; Zbl 0837.12006)] established o-minimality of the real field augmented by exponentiation and all restricted analytic functions using the theory of Hardy fields and some non-trivial facts on quantifier elimination. The paper under review can be seen as a very interesting step towards generalization of the o-minimality results mentioned above.
reviewed by: Zbigniew Hajto
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 12L12
zbMATH DE Number: 1423616
zbMATH Keywords: Hardy field
zbMATH Keywords: valuation
zbMATH Keywords: H-couple
zbMATH Keywords: quantifier elimination
zbMATH Keywords: model completion
MaRDI profile type: Publication
OpenAlex ID: W1996490280
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DOI: 10.1006/JABR.1999.8128
description: scientific article; zbMATH DE number 1423616