非赋值结构的对偶理论
A theory of pairs for non-valuational structures
摘要：
给定一个弱o-极小结构$\mathcal M$及其o-极小完备化$\bar {\mathcal M}$，首先将$\bar {\mathcal M}$与一个规范语言联系起来，然后证明$Th(\mathcal M)$决定$Th(\bar {\mathcal M})$ .然后，我们调查的理论对$\mathcal M^P=(\bar {\mathcal M};M)$的精神，理论的密集对o-最小的结构，并证明，除其他结果外，它是近模型完整的，和每个$\mathcal M^P$ -可定义的开放子集的$\bar M^n$已经定义在$\bar {\mathcal M}$。我们给出了一个弱O-极小结构的例子，它解释了$\bar {\mathcal M}$，并表明，它是不是elementarily等价于任何约简的O-极小迹。
英文摘要：
Given a weakly o-minimal structure $\mathcal M$ and its o-minimal completion $\bar {\mathcal M}$, we first associate to $\bar {\mathcal M}$ a canonical language and then prove that $Th(\mathcal M)$ determines $Th(\bar {\mathcal M})$. We then investigate the theory of the pair $\mathcal M^P=(\bar {\mathcal M};M)$ in the spirit of the theory of dense pairs of o-minimal structures, and prove, among other results, that it is near model complete, and every $\mathcal M^P$-definable open subset of $\bar M^n$ is already definable in $\bar {\mathcal M}$. We give an example of a weakly o-minimal structure which interprets $\bar {\mathcal M}$ and show that it is not elementarily equivalent to any reduct of an o-minimal trace.
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