论文标题
俱乐部固定反射和其他组合原理，$ \ aleph_ {ω+2} $
Club Stationary Reflection and other Combinatorial Principles at $\aleph_{ω+2}$
论文作者
论文摘要
在本文中，我们继续在双重后继者的紧凑性和不兼容原理的[吉尔顿 - 屋子 - 史加洛娃]中进行研究，重点是可计数cofination的双重继承者。我们获得了满足这些双重继任者树木财产和俱乐部固定反射的模型。此外，我们还可以获得可接近性或失败。我们还展示了如何通过合并倒塌来获得$ \ aleph_ {ω+2} $上的结果；在这些情况下尤其重要的是我们的一种不可约束的定理，表明满足某些链接假设的POSET可以保留俱乐部的固定反射。
In this paper we continue the study in [Gilton-Levine-Stejskalova] of compactness and incompactness principles at double successors, focusing here on the case of double successors of singulars of countable cofinality. We obtain models which satisfy the tree property and club stationary reflection at these double successors. Moreover, we can additionally obtain either approachability or its failure. We also show how to obtain our results on $\aleph_{ω+2}$ by incorporating collapses; particularly relevant for these circumstances is a new indestructibility theorem of ours showing that posets satisfying certain linked assumptions preserve club stationary reflection.
