论文标题
DP-Finite Fields V：有限重量的拓扑字段
Dp-finite fields V: topological fields of finite weight
论文作者
论文摘要
我们证明，不稳定的DP-FINITE领域承认可定义的V-Topologies。结果，DP-FINITE场的Henselian猜想意味着Shelah的猜想是DP-FINITE场的猜想。从概念上讲，这可以更简单地证明了积极特征的DP-FINITE领域的分类。 对于$ n \ ge 1 $，我们定义了一个本地类“ $ W_n $ - topological Fields”，概括V-Topological Fields。 $ W_1 $ - 学术与V-Topology是同一件事，而$ W_N $ - 学术是一些更高的类似物。如果$ k $是一个不稳定的DP-FINITE字段，则规范拓扑是$ n = \ operatatorName {dp-rk}（k）$的可定义的$ W_N $ -TOPOLOGY。每个$ w_n $ -Topology具有1到$ n $ coarsenings，这是V-Topology。如果给定的$ W_N $ - 学术在某些结构上是可以定义的，那么V-Topological Coarsenings也是如此。
We prove that unstable dp-finite fields admit definable V-topologies. As a consequence, the henselianity conjecture for dp-finite fields implies the Shelah conjecture for dp-finite fields. This gives a conceptually simpler proof of the classification of dp-finite fields of positive characteristic. For $n \ge 1$, we define a local class of "$W_n$-topological fields", generalizing V-topological fields. A $W_1$-topology is the same thing as a V-topology, and a $W_n$-topology is some higher-rank analogue. If $K$ is an unstable dp-finite field, then the canonical topology is a definable $W_n$-topology for $n = \operatorname{dp-rk}(K)$. Every $W_n$-topology has between 1 and $n$ coarsenings that are V-topologies. If the given $W_n$-topology is definable in some structure, then so are the V-topological coarsenings.
