标题： $\widetilde{\mid}\hspace{1mm}$- 超滤子的可除性 II：整体图景 显示英文标题

标题： $\widetilde{\mid}\hspace{1mm}$-divisibility of ultrafilters II: The big picture

摘要： 一个超滤子上的可除性关系定义如下：${\cal F}\hspace{1mm}\widetilde{\mid}\hspace{1mm}{\cal G}$当且仅当每个属于$\cal F$且对于可除性向上封闭的集合也属于$\cal G$。在描述了这个拟序的前$\omega$个层次之后，本文我们推广了确定超滤子的基本除数的过程。首先我们描述这些基本除数，它们作为素超滤子的幂（等价类）得到。使用非标准分析的方法，我们确定了超滤子的模式：其基本除数的集合以及每个除数的重数。所有这样的模式在适当的拓扑中具有某种闭包性质。我们分离出属于具有给定模式的每个超滤子的集合族。最后，我们证明具有闭包性质的每个模式都被某个超滤子实现。 显示英文摘要

摘要： A divisibility relation on ultrafilters is defined as follows: ${\cal F}\hspace{1mm}\widetilde{\mid}\hspace{1mm}{\cal G}$ if and only if every set in $\cal F$ upward closed for divisibility also belongs to $\cal G$. After describing the first $\omega$ levels of this quasiorder, in this paper we generalize the process of determining the basic divisors of an ultrafilter. First we describe these basic divisors, obtained as (equivalence classes of) powers of prime ultrafilters. Using methods of nonstandard analysis we determine the pattern of an ultrafilter: the collection of its basic divisors as well as the multiplicity of each of them. All such patterns have a certain closure property in an appropriate topology. We isolate the family of sets belonging to every ultrafilter with a given pattern. Finally, we show that every pattern with the closure property is realized by an ultrafilter.