THE TREE PROPERTY UP TO אω+1
THE TREE PROPERTY UP TO אω+1
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树的性质高达 אω+1
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
I. Neeman
中科院分区：
文献类型：
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作者：
I. Neeman
摘要 假设 ω 超紧基数，我们强制获得一个模型，其中树属性同时满足 אω+1 和 אn（对于所有 2 ≤ n < ω）。前者的模型是由 Magidor-Shelah 从一个大基数之上的大基数假设中获得的，最近是由 Sinapova 从 ω 超紧基数获得的。 Cummings-Foreman 从 ω 超紧基数获得了后者的模型。我们的模型，两者同时成立，是朝着在越来越大的后继基数间隔上获得树属性的目标迈出的又一步。
Abstract Assuming ω supercompact cardinals we force to obtain a model where the tree property holds both at אω+1, and at אn for all 2 ≤ n < ω. A model with the former was obtained by Magidor–Shelah from a large cardinal assumption above a huge cardinal, and recently by Sinapova from ω supercompact cardinals. A model with the latter was obtained by Cummings–Foreman from ω supercompact cardinals. Our model, where the two hold simultaneously, is another step toward the goal of obtaining the tree property on increasingly large intervals of successor cardinals.