H-fields and their Liouville extensions
H-fields and their Liouville extensions
复制标题
H 场及其刘维尔扩展
DOI：
10.1007/s002090000358
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发表时间：
2002
影响因子：
0.8
通讯作者：
Lou van den Dries
中科院分区：
文献类型：
--
作者：
Matthias Aschenbrenner;Lou van den Dries
抽象的。我们引入H-域作为某种类型的有序微分域。哈代域扩张
${\mathbb R}$，以及在
${\mathbb R}$是H域。我们研究的刘维尔扩展的范畴内的H-域，作为一个步骤的模型理论的H-域。主要结果是，一个H场最多有两个刘维尔闭包。
Abstract. We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending
${\mathbb R}$, as well as the field of logarithmic-exponential series over
${\mathbb R}$ are H-fields. We study Liouville extensions in the category of H-fields, as a step towards a model theory of H-fields. The main result is that an H-field has at most two Liouville closures.