Real closed rings. II. Model theory. (English) Zbl 0538.03028

This paper concerns the model theory of real closed rings, which are the convex subrings of real closed fields. Much follows directly from the Ax- Kochen/Ershov theorem. An explicit quantifier elimination procedure is also given. Such rings occur in nature as residue rings modulo certain prime ideals of rings of continuous functions. This was the subject of Part I, which is still to appear. Dickmann recently showed that such rings arise also as residue rings of continuous semialgebraic functions on curves. J. Moloney has found many other decidable theories of rings occurring in the context of Part I.


03C60 Model-theoretic algebra
03C10 Quantifier elimination, model completeness, and related topics
13J25 Ordered rings
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