\(H\)-fields and their Liouville extensions (Q1433429)

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)].