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Existence of tamely ramified tower of extension over $\mathbb{Q}_p$
Let $p$ be a prime. There exist following containment : $$\mathbb{Q}_p \subset \mathbb{Q}_p^{\rm nr} \subset \mathbb{Q}_p^{\rm tr} \subset \overline{\mathbb{Q}}_p$$
Here $\mathbb{Q}_p^{\rm nr}$ and $\ …