论文标题
liouville关闭$ h_t $ -fields
Liouville closed $H_T$-fields
论文作者
论文摘要
令$ t $为O-Wimimal理论，扩展了真实封闭订购的字段的理论。 $ h_t $ -field是配备$ t $衍生的$ k $ $ k $ $ t $，因此$ k $的基础订购差异字段是$ h $ field。我们研究$ h_t $ - 场及其扩展。我们的主要结果是，如果$ t $是电源的，那么每个$ h_t $ - field $ k $都具有一个或两个最小的liouville关闭$ h_t $ field扩展，最高$ k $ iSomorphism。可以放松功率界限的假设以允许某些指数案例，例如$ t = \ operatatorName {th}（\ mathbb {r} _ {\ operatoratorname {an}，\ exp}）$。
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 $T = \operatorname{Th}(\mathbb{R}_{\operatorname{an},\exp})$.
