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I just want to ask if anybody as any examples of a first order model complete theorie of henselian local rings which is not some theory of valuation rings. More precisely-

I am looking for a theory $T$ of the language of rings such that

  1. Every model of $T$ is a henselian local ring
  2. There exists a model of $T$ that is not a valuation ring
  3. $T$ is model complete.

Indeed, does anybody know anything about that model theory of henselian local rings?

Thanks for your help in advance.

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Are all local henselian rings domains to you? Otherwise, I'd try to find a theory of local henselian rings which are not domains. Unless those don't exist for some reason. :) – tomasz Dec 18 '12 at 20:13

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