Liouville闭$H_T$ -域
Liouville closed $H_T$-fields
摘要：
设$T$是实封闭的序域理论的一个o-极小理论. $H_T$ -域是配备有$T$ -导出的$T$的模型$K$，使得$K$的基础有序微分域是$H$ -域。研究了$H_T$ -域及其扩张.我们的主要结果是，如果$T$是幂有界的，那么每个$H_T$ -域$K$都有恰好一个或恰好两个极小Liouville闭$H_T$ -域扩张直到$K$ -同构.幂有界性的假设可以放宽，以允许某些指数情况，如$T = \operatorname{Th}(\mathbb{R}_{\operatorname{an},\exp})$。
英文摘要：
Let $T$ be an o-minimal theory extending the theory of real closed ordered fields. An $H_T$-field is a model $K$ of $T$ equipped with a $T$-derivation such that the underlying ordered differential field of $K$ is an $H$-field. We study $H_T$-fields and their extensions. Our main result is that if $T$ is power bounded, then every $H_T$-field $K$ has either exactly one or exactly two minimal Liouville closed $H_T$-field extensions up to $K$-isomorphism. The assumption of power boundedness can be relaxed to allow for certain exponential cases, such as $T = \operatorname{Th}(\mathbb{R}_{\operatorname{an},\exp})$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
