实域展开式中整数集的闭离散集定义
Defining the set of integers in expansions of the real field by a closed discrete set
摘要：
设D \subseteq \mathbb{R}是闭的离散的，f：D^n \to \mathbb{R}使得f（D^n）在某处稠密。我们证明了（\mathbb{R}，+，\cdot，f）定义了整数的集合.作为一个应用，我们得到了对每个a，b \in \mathbb{R} with \log_{a}（b）\notin \mathbb{Q}，由a和b生成的两个循环乘法子群展开的实域定义了整数集.
英文摘要：
Let D\subseteq \mathbb{R} be closed and discrete and f:D^n \to \mathbb{R} be such that f(D^n) is somewhere dense. We show that (\mathbb{R},+,\cdot,f) defines the set of integers. As an application, we get that for every a,b \in \mathbb{R} with \log_{a}(b)\notin \mathbb{Q}, the real field expanded by the two cyclic multiplicative subgroups generated by a and b defines the set of integers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
