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Jan 24, 2015 at 20:04 comment added user21349 The product of two Laurent series need not be a Laurent series. If you want a non-archimedean field that has well-defined multiplication and division, a good candidate is the Levi-Civita field, but the LC field doesn't have $e^\omega$ where $\omega$ is infinite. It would also be odd if a structure as "natural" as the Laurent series were isomorphic to the hyperreals, since the hyperreals are non-unique in ZFC.
Jan 24, 2015 at 14:55 comment added Ross Millikan This is also asked at math.stackexchange.com/questions/1117477/…
Jan 24, 2015 at 14:29 answer added Joel David Hamkins timeline score: 12
Jan 24, 2015 at 12:50 vote accept Anixx
Jan 24, 2015 at 12:31 answer added Todd Trimble timeline score: 14
Jan 24, 2015 at 10:32 history edited Anixx CC BY-SA 3.0
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Jan 24, 2015 at 10:26 history asked Anixx CC BY-SA 3.0