All Questions

Let $K$ be an unramified extension of the $p$-adic number field $\mathbb{Q}_p$. Suppose we have a tower of extensions: $$K=:K(u_0) \subset K(u_1) \subset K(u_2) \subset K(u_3) \subset \cdots \subset ...

Given a local field $K$ with absolute Galois group $\Gamma$. Is it "possible" to define the upper numbering on $\Gamma$ without using the lower numbering? In other words, given $\gamma \in \...