We continue the study of Rosenthal families initiated by Damian Sobota. We show that every Rosenthal filter is the intersection of a finite family of ultrafilters that are pairwise incomparable in the Rudin-Keisler partial ordering of ultrafilters. We introduce a property of filters, called an \(r\)-filter, properly between a selective filter and a \(p\)-filter. We prove that every \(r\)-ultrafilter is a Rosenthal family. We prove that it is consistent with ZFC to have uncountably many \(r\)-ultrafilters such that any intersection of finitely many of them is a Rosenthal filter.

我们继续研究由达米安·索博塔 (Damian Sobota) 发起的罗森塔尔家族。我们表明，每个 Rosenthal 过滤器都是有限超过滤器族的交集，这些超过滤器在超过滤器的 Rudin-Keisler 偏序中是成对不可比的。我们在选择性过滤器和\(p\)过滤器之间引入了过滤器的一个属性，称为\(r\) -过滤器 。我们证明每个\(r\) -ultrafilter 都是一个 Rosenthal 家族。我们证明了具有不可数多个\(r\) -ultrafilters 的ZFC 是一致的，使得它们中的有限多个的任何交集都是 Rosenthal 过滤器。