论文标题
关于苏斯林树及其通用树枝的刚性
On the rigidity of Souslin trees and their generic branches
论文作者
论文摘要
我们表明，有一个Souslin Tree $ s $是一致的，使得用$ S $，$ s $是kurepa，对于所有俱乐部，$ c \ subsetω_1$，$ s \ upharpoonRight c $ cug arigid arigid。这在俱乐部的僵化程度和几乎是库尔帕树的俱乐部学位上回答了福茨的问题。此外，我们表明它与$ \ diamondsuit $是一致的，对于每条souslin树来说，都有一个密集的$ x \ subset s $，它没有$ s $的副本。这与鲍姆加特纳引起的问题有关。
We show it is consistent that there is a Souslin tree $S$ such that after forcing with $S$, $S$ is Kurepa and for all clubs $C \subset ω_1$, $S\upharpoonright C$ is rigid. This answers Fuchs's questions in Club degrees of rigidity and almost Kurepa trees. Moreover, we show it is consistent with $\diamondsuit$ that for every Souslin tree there is a dense $X \subset S$ which does not have a copy of $S$. This is related to a question due to Baumgartner.
