Model theory of real closed ringsAlexander
نویسنده
چکیده
We show that the class of real closed rings is an elementary class, i.e., it can be axiomatized in the rst order language of rings. Adding a binary`radical relation' which encodes information about the spectrum, we prove that the theory of real closed rings as well as the theory of real closed domains admit a model companion. In the rst case the model companion consists of certain von Neumann regular rings, in the second case it consists of certain real closed valuation rings.
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