论文标题
Aronszajn树保护和有限强迫公理
Aronszajn tree preservation and bounded forcing axioms
论文作者
论文摘要
我研究了强迫类$γ$的三个反射原则层次结构之间的关系：有限强迫公理的层次结构，$σ^1_1 $ -Absoluteness和Aronszajn树保护原则。 $κ$的后者原理说，每当$ t $是一棵高度$ω_1$和宽度$κ$时，没有订单类型$ω_1$的分支，并且每当$ p $是$γ$中的强迫概念时，就不会有$ p $ p $ p $ t $ t $ t $具有这样的分支。 $σ^1_1 $ -Absoluteness用作这些原理和有限强迫公理之间的中介。主要结果的一个特殊情况是，对于强迫不添加真实的类的类，$ 2^ω$的三个原则是等效的。特别注意某些子集合强迫的子类，因为这些是自然的强迫类，这些类别不会增加真实。
I investigate the relationships between three hierarchies of reflection principles for a forcing class $Γ$: the hierarchy of bounded forcing axioms, of $Σ^1_1$-absoluteness and of Aronszajn tree preservation principles. The latter principle at level $κ$ says that whenever $T$ is a tree of height $ω_1$ and width $κ$ that does not have a branch of order type $ω_1$, and whenever $P$ is a forcing notion in $Γ$, then it is not the case that $P$ forces that $T$ has such a branch. $Σ^1_1$-absoluteness serves as an intermediary between these principles and the bounded forcing axioms. A special case of the main result is that for forcing classes that don't add reals, the three principles at level $2^ω$ are equivalent. Special attention is paid to certain subclasses of subcomplete forcing, since these are natural forcing classes that don't add reals.
