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Exercise 5 .39 page 46 Real and Abstract Analysis [Hewitt and Stromberg]

How to show that every non-Archimedian field contains a subfield algebraically and order isomorphic to $\mathbb{Q}(t)$, where $\mathbb{Q}(t)$ is the field of rational functions with coefficient in ...
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Archimedean ordered fields and valuations (exercise)

Definitions: Let $(K,\leq)$ be a totally ordered field and $(G,\leq)$ a totally ordered abelian group (written additively). If we denote $\mathbb{Z}a\!=\!\{na;\, n\!\in\!\mathbb{Z}\}$, then $G$ is ...