Aschenbrenner, Matthias; van den Dries, Lou \(H\)-fields and their Liouville extensions. (English) Zbl 1066.12002 Math. Z. 242, No. 3, 543-588 (2002). The authors introduce the notion of \(H\)-field in order to study relations between Hardy fields and the fields of logarithmic-exponential series. In the category of \(H\)-fields it is possible to define Liouville extensions and Liouville closures. The main result of the paper is a theorem that for an \(H\)-field there exist at most two Liouville closures. The paper is the second in a series of papers by the same authors related with the model theory of ordered differential fields. For the first see [J. Algebra 225, No.1, 309-358 (2000; Zbl 0974.12015)]. Reviewer: Zbigniew Hajto (Kraków) Cited in 7 ReviewsCited in 14 Documents MSC: 12H05 Differential algebra 03C10 Quantifier elimination, model completeness, and related topics Keywords:H-fields; Hardy fields; Liouville extensions; LE-series; model completion Citations:Zbl 0974.12015 PDFBibTeX XMLCite \textit{M. Aschenbrenner} and \textit{L. van den Dries}, Math. Z. 242, No. 3, 543--588 (2002; Zbl 1066.12002) Full Text: DOI