论文标题
专门为小近似树木II
Specialising Trees With Small Approximations II
论文作者
论文摘要
我们表明，常规的红衣主教$λ$上的一种众所周知的理想存在意味着紧凑型属性，涉及一棵高度$λ$的特殊性，而没有辅助分支。我们还使用Neeman的侧面条件方法表明，这种理想的存在与许多适当的猜测模型是一致的。这些对象足以扩展\ cite {mhpr_spe}的主要定理：一个人可以使用$ {<}κ$ clucked，$κ^{+} $ - proper，$κ^{+} $ - proper和$κ^{++} $ youm-yim-lotter-obly oppersity，可以将任何高度$κ^{++} $的无分支树进行专业化。
We show that the existence of a well-known type of ideals on a regular cardinal $λ$ implies a compactness property concerning the specialisability of a tree of height $λ$ with no cofinal branches. We also use Neeman's method of side conditions to show that the existence of such ideals is consistent with stationarily many appropriate guessing models. These objects suffice to extend the main theorem of \cite{mhpr_spe}: one can generically specialise any branchless tree of height $κ^{++}$ with a ${<}κ$-closed, $κ^{+}$-proper, and $κ^{++}$-preserving forcing, which has the $κ^+$-approximation property.
