Model Theory of Real Closed Rings
Model Theory of Real Closed Rings
复制标题
实闭环模型理论
DOI：
10.1090/fic/032/17
复制
发表时间：
2007
影响因子：
0.9
通讯作者：
A. Prestel
中科院分区：
文献类型：
--
作者：
A. Prestel
我们证明了真实的闭环类是一个基本类，即，它可以用环的一阶语言来公理化。添加一个二进制的'激进的关系'，它编码的频谱信息，我们证明了理论的真实的闭环以及理论的真实的闭域承认一个模型伴侣。在第一种情况下，模型伴侣由某些冯·诺依曼正则环组成，在第二种情况下，它由某些真实的闭赋值环组成。
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.