论文标题
繁殖算术中乘法的不确定性和一组力量
Undefinability of multiplication in Presburger arithmetic with sets of powers
论文作者
论文摘要
首先，我们证明了一组或多种功率的任何可定义的图像的自然密度为零。然后，通过调整二分法的证明，弗里德曼和米勒对O最低结构的二分法，我们产生了类似的二分法，以扩大整数上的爆炸前算术。结合这两个结果，我们获得了按任意数量的整数组合组的扩展不会定义乘法。
We begin by proving that any Presburger-definable image of one or more sets of powers has zero natural density. Then, by adapting the proof of a dichotomy result on o-minimal structures by Friedman and Miller, we produce a similar dichotomy for expansions of Presburger arithmetic on the integers. Combining these two results, we obtain that the expansion of the ordered group of integers by any number of sets of powers does not define multiplication.
