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
- Every model of $T$ is a henselian local ring
- There exists a model of $T$ that is not a valuation ring
- $T$ is model complete.
Indeed, does anybody know anything about that model theory of henselian local rings?
Thanks for your help in advance.