Talk:Hahn embedding theorem

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Sources[edit]

The version of the article I edited had some problems, mostly being unsourced and (to me) unverifiable. I changed it to be sourced, but perhaps destroyed some (slightly false I suspect, but probably correctable) points, and the sources are still paper only.

I think the original is not currently digitized. Apparently number 3 of vol 116 was digitized, but number 2a (the issue containing Hahn's paper) was not. Perhaps someone can confirm using his collected works, ISBN 9783211826829, page 439-444 and 445-500 or so.

At any rate, the version of this page I edited mentioned something about embedding in a real-closed field instead of into a vector space (of easily uncountable dimension) over the reals. The Zbl review mentions nothing about the field, and confirms the version I put in this article (the vector space version). However, this seems only mildly related to Hölder's theorem on archimedian ordered groups being subgroups of the real fields.

There was a history (MR2206281) of non-archimedian mathematics that seemed to suggest that Hahn's work gave a theoretic backing to non-archimedian groups, and it would certainly be convenient for that theory if Hahn's theorem could be strengthened to the old version in this article.

Alternatively, any standard text on ordered algebraic structures would probably be a better source. Fuchs has a few books on ordered algebraic structures, but I only had his valuation books at hand, and just took the one that was still in print. It only gives the vector space version. JackSchmidt (talk) 04:36, 11 January 2009 (UTC)