论文标题
在与有价值的领域相关的超级场上
On the hyperfields associated to valued fields
论文作者
论文摘要
一个人可以以自然的方式将有价值的Hyperfields $（\ Mathcal {h} _i）_ {i \ in i} $的价值逆系统关联到一个有价值的字段。相反，我们调查了这种系统何时来自一个有价值的领域。首先，我们通过证明某些系统的倒数限制是严格的高场高场，扩展了Krasner的结果。其次，我们描述了一种类似于哈恩的结构，该结构从严格的高菲尔德（Hyperfield）产生了一个亨斯尔（Henselian）有价值的田地。此外，我们以一种由两个二进制函数符号$ \ oplus $和$ \ cdot $和两个常数符号和两个常数符号$ \ textbf {0} $和$ \ textbf {1} $组成的语言的严格有价值高场理论的公理化。
One can associate to a valued field an inverse system of valued hyperfields $(\mathcal{H}_i)_{i \in I}$ in a natural way. We investigate when, conversely, such a system arise from a valued field. First, we extend a result of Krasner by showing that the inverse limit of certain systems are stringent valued hyperfields. Secondly, we describe a Hahn-like construction which yields a henselian valued field from a stringent valued hyperfield. In addition, we provide an axiomatisation of the theory of stringent valued hyperfields in a language consisting of two binary function symbols $\oplus$ and $\cdot$ and two constant symbols $\textbf{0}$ and $\textbf{1}$.
