广义对称系统与薄-很高紧散布空间
Generalized symmetric systems and thin-very tall compact scattered spaces
摘要：
我们解决了一个著名的问题，在理论上的紧凑的分散空间和超原子布尔代数表明，在GCH和每个正则基数$κ\geq ω$，有一个偏序集$\mathcal P_κ$保持所有的基数，并迫使存在一个$κ$ -薄非常高的局部紧凑的分散空间。对于$κ> ω$，我们将偏序集$\mathcal P_κ$设想为偏序集$\mathcal P_ω$的高级类似物，该偏序集最初是在（未发表的）替代一致性证明的上下文中由Bagaria和Bagaria引入的。
英文摘要：
We solve a well--known problem in the theory of compact scattered spaces and superatomic boolean algebras by showing that, under GCH and for each regular cardinal $κ\geq ω$, there is a poset $\mathcal P_κ$ preserving all cardinals and forcing the existence of a $κ$--thin very tall locally compact scattered space. For $κ> ω$, we conceive the poset $\mathcal P_κ$ as a higher analogue of the poset $\mathcal P_ω$ originally introduced by Asperó and Bagaria in the context of an (unpublished) alternative consistency proof.
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