超滤子的乘法有限嵌入性与可分性
Multiplicative finite embeddability vs divisibility of ultrafilters
摘要：
我们继续探索各个方面的可分性的超滤子，增加一个关系的图片：乘法有限嵌入。我们表明，它位于之间的整除关系$\mid_M$和$\widetilde{\mid}$。它的极小元的集合被证明是非常丰富的，并且使用$\widetilde{\mid}$ -层次结构来得到这种丰富性的更好的直观。我们发现的地方的一套$\widetilde{\mid}$ -极大超滤子之间的一些已知的家庭超滤子。最后，我们引入了新的概念，大的子集的$\mathbb{N}$，并比较它与其他这样的概念，重要的无限组合学和拓扑动力学。
英文摘要：
We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations $\mid_M$ and $\widetilde{\mid}$. The set of its minimal elements proves to be very rich, and the $\widetilde{\mid}$-hierarchy is used to get a better intuition of this richness. We find the place of the set of $\widetilde{\mid}$-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of subsets of $\mathbb{N}$, and compare it to other such notions, important for infinite combinatorics and topological dynamics.
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。
