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Easton's theorem for the tree property below ℵω
Annals of Pure and Applied Logic ( IF 0.8 ) Pub Date : 2021-04-06 , DOI: 10.1016/j.apal.2021.102974
Šárka Stejskalová

Starting with infinitely many supercompact cardinals, we show that the tree property at every cardinal n, 1<n<ω, is consistent with an arbitrary continuum function below ω which satisfies 2n>n+1, n<ω. Thus the tree property has no provable effect on the continuum function below ω except for the restriction that the tree property at κ++ implies 2κ>κ+ for every infinite κ.



中文翻译:

伊斯顿定理树酒店楼下ℵ ω

从无限多个超紧缩基数开始,我们证明了每个基数的树属性 ñ1个<ñ<ω,与下面的任意连续函数一致 ω 满足 2个ñ>ñ+1个ñ<ω。因此,树的属性对下面的连续函数没有可证明的影响ω 除了tree属性位于 κ++ 暗示 2个κ>κ+对于每个无限大的κ

更新日期:2021-04-13
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