O-最小结构：低元数与代数
O-minimal structures: low arity versus generation
摘要：
我们证明了Hilbert第十三问题的一个类似问题在实次解析情形下是失败的，即我们证明了对于任意整数$n$，由$n$变量中的限制解析函数生成的o-极小结构严格小于所有全局次解析集的结构，而这两种结构在$\mathbb R ^{n+1}$中定义了相同的子集.
英文摘要：
We show that an analogue of the Hilbert's Thirteenth Problem fails in the real subanalytic setting.Namely we prove that, for any integer $n$, the o-minimal structure generated by restricted analytic functions in $n$ variables is strictly smaller than the structure of all global subanalytic sets, whereas these two structures define the same subsets in $\mathbb R ^{n+1}$.
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