I need a reference (different from Hahn's 1907 paper) for the following result.

Theorem:If $G$ is a totally ordered abelian group, then the field $\mathbb{R}((G))$ is archimedean complete.

- $\mathbb{R}((G))$ consists of all the functions $f:G\to\mathbb{R}$ such that $\{g\in G:f(g)\neq0\}$ is well-ordered.
- Let $E$ be an ordered field. Two nonzero elements $x,y\in E$ are
*comparable*if there exist $m,n\in\mathbb{N}$ such that $|x|<m|y|$ and $|y|<n|x|$ (where $|a|$ is defined as $\max\{a,-a\}$). - Let $E/ K$ be an extension of ordered fields, where the order on $E$ restricted to $K$ coincides with that of $K$. We say that $E$ is an
*Archimedean extension of $K$*if for every $x\in E$, there exists $y\in K$ such that $x$ and $y$ are comparable in $E$. - A field $K$ is
*Archimedean complete*if it has no proper archimedean extension fields.

Does anyone know a good reference for the proof of this result? The more the better.