Laver模型中的点余有限覆盖
Point-cofinite covers in the Laver model
摘要：
设S1（Gamma，Gamma）是这样的陈述：对于每个点上有限开覆盖序列，可以从每个覆盖中选取一个元素并得到一个点上有限覆盖。b是不满足S1（Gamma，Gamma）的实数集的最小基数。我们证明了以下断言：（1）如果存在一个无界塔，则存在基数为b的实数集，满足S1（Gamma，Gamma）。(2)所有满足S1（Gamma，Gamma）的实数集的基数小于b是相容的。这些结果也可以表示为连续实值函数空间的Arhangel'skii性质α_2。主要的技术结果是，在拉弗模型中，基数b的每一组实在贝尔空间w^w中都有一个无界的博雷尔像。
英文摘要：
Let S1(Gamma,Gamma) be the statement: For each sequence of point-cofinite open covers, one can pick one element from each cover and obtain a point-cofinite cover. b is the minimal cardinality of a set of reals not satisfying S1(Gamma,Gamma). We prove the following assertions: (1) If there is an unbounded tower, then there are sets of reals of cardinality b, satisfying S1(Gamma,Gamma). (2) It is consistent that all sets of reals satisfying S1(Gamma,Gamma) have cardinality smaller than b. These results can also be formulated as dealing with Arhangel'skii's property alpha_2 for spaces of continuous real-valued functions. The main technical result is that in Laver's model, each set of reals of cardinality b has an unbounded Borel image in the Baire space w^w.
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