On the Size of Closed Unbounded Sets
On the Size of Closed Unbounded Sets
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DOI：
10.1016/0168-0072(91)90047-p
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发表时间：
1991-11
期刊：
影响因子：
--
通讯作者：
J. Baumgartner
中科院分区：
文献类型：
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作者：
J. Baumgartner
我们研究了[λ]<κ的封闭无界子集的大小的各个方面，包括基数，特别是当λκ+ ε ω时。这个问题被解决为研究某些平稳集的大小。相对于ω1-Erdös基数的存在性，证明了ωω3< ωω13和[ω3]<ω2的每一个闭合无界子集具有ωω13的基数是一致的。定义了ω1-Erdös性质ω -显著性的减弱，并表明在施加于ω1-Erdös基数的一大类类似伊斯顿的强迫下，ω -显著性仍然存在。还描述了一类保留α-Erdösness的逆伊斯顿力，并特别注意了□-原理的建立。
We study various aspects of the size, including the cardinality, of closed unbounded subsets of [λ]<κ, especially when λ κ+nfornϵ ω. The problem is resolved into the study of the size of certain stationary sets. Relative to the existence of an ω1-Erdös cardinal it is shown consistent that ωω3< ωω13and every closed unbounded subsetof [ω3]<ω2has cardinality ωω13. A weakening of the ω1-Erdös property, ω1-remarkability, is defined and shown to be retained under a large class of Easton-like forcings applied to ω1-Erdös cardinals. A class of reverse-Easton forcings preserving α-Erdösness is also described, with special attention to the establishment of □-principles.