Dominating Projective Sets in the Baire Space
Dominating Projective Sets in the Baire Space
复制标题
贝尔空间中的主导射影集
DOI：
10.1016/0168-0072(94)90025-6
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
O. Spinas
中科院分区：
文献类型：
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作者：
O. Spinas
我们证明了Baire空间中的每个解析集都包含一个均匀树的分支，即一个超完美树，它具有这样的性质：对于每个splitnode，所有后继splitnode都具有相同的长度。我们称解析集的这一性质为超正则性，但我们指出，一致树的概念并不足以刻画一般的支配解析集。我们构造了一个控制闭集，它的性质是：对于任何一个分支包含在闭集中的一致树，这些分支的集合都是控制的。我们还证明了从一个1 n +1-快速滤子可以构造一个非u-正则的1 n-集。最后证明了∑12-Kσ-正则性蕴涵∑12-u-正则性。
We show that every analytic set in the Baire space which is dominating contains the branches of auniform tree,i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. We call this property of analytic setsu-regularity.However, we show that the concept of uniform tree does not suffice to characterize dominating analytic sets in general. We construct a dominating closed set with the property that for no uniform tree whose branches are contained in the closed set, the set of these branches is dominating. We also show that from aΣ1n+1-rapid filter a non-u-regular Π1n-set can be constructed. Finally, we prove that ∑12-Kσ-regularity implies ∑12-u-regularity.