标题： 在自由Suslin树上的强迫 显示英文标题

标题： Forcing Over a Free Suslin Tree

摘要： 我们引入了一个抽象框架，用于在自由Suslin树上使用乘积强制的子序进行强制，该乘积强制通过可数逼近为树添加某些结构。 该框架的主要思想是相容性、分离性和关键性质。 我们给出了该框架的三个应用：对自由Suslin树的导出树进行专门化，向自由Suslin树中添加不可数的几乎不相交子树，以及向自由Suslin树中添加几乎不相交的自同构。 使用自同构强制，我们构造了一个模型，在该模型中存在一个几乎Kurepa的Suslin树和一个非饱和的Aronszajn树，并且不存在Kurepa树。 该模型解决了Bilaniuk、Moore、Jin和Shelah提出的一些开放问题。 显示英文摘要

摘要： We introduce an abstract framework for forcing over a free Suslin tree with suborders of products of forcings which add some structure to the tree using countable approximations. The main ideas of this framework are consistency, separation, and the Key Property. We give three applications of this framework: specializing derived trees of a free Suslin tree, adding uncountable almost disjoint subtrees of a free Suslin tree, and adding almost disjoint automorphisms of a free Suslin tree. Using the automorphism forcing, we construct a model in which there is an almost Kurepa Suslin tree and a non-saturated Aronszajn tree, and there does not exist a Kurepa tree. This model solves open problems due to Bilaniuk, Moore, and Jin and Shelah.