Closed asymptotic couples
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.
scientific article; zbMATH DE number 1423616
scientific article