论文标题
稳定嵌入的henselian价值领域的子模型
Stably embedded submodels of Henselian valued fields
论文作者
论文摘要
我们显示了该属性的转移原理，在给定基本扩展中实现的所有类型都是可以定义的。它可以写如下：当且仅当其值组稳定地嵌入其相应的扩展中时，将Henselian Reedure字段稳定地嵌入了基础扩展中，其残基场稳定地嵌入其相应的扩展中，并且值的延伸范围可满足某个代数条件。例如，我们显示Hahn字段上的所有类型$ \ Mathbb {r}（（（\ Mathbb {Z}））$都是可定义的。同样，Witt环$ W（\ Mathbb {f} _p^{\ text {alg}}）$上的所有类型都是可定义的。这扩展了CBIDES和DELON以及CBIDES和YE的作品。
We show a transfer principle for the property that all types realised in a given elementary extension are definable. It can be written as follows: a Henselian valued fields is stably embedded in an elementary extension if and only if its value group is stably embedded in its corresponding extension, its residue field is stably embedded in its corresponding extension, and the extension of valued fields satisfies a certain algebraic condition. We show for instance that all types over the Hahn field $\mathbb{R}((\mathbb{Z}))$ are definable. Similarly, all types over the quotient field of the Witt ring $W(\mathbb{F}_p^{\text{alg}})$ are definable. This extends a work of Cubides and Delon and of Cubides and Ye.
