Analytic Ideals and Their Applications
Analytic Ideals and Their Applications
复制标题
分析理想及其应用
DOI：
10.1016/s0168-0072(98)00051-7
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发表时间：
1999
影响因子：
0.8
通讯作者：
Slawomir Solecki
中科院分区：
文献类型：
--
作者：
Slawomir Solecki
研究了自然数子集的解析理想的结构。例如，我们证明了对于解析理想I，理想{X <$（Ω × Ω：<$En X <$（{0，1，.，n} × Ω }）在I之下是Rudin-Keisler，或者I是由一个下连续子测度非常简单地诱导的。此外，我们表明，类的理想，以这种方式诱导的lsc子措施与Polishable理想，以及分析P-理想相吻合。我们研究这类理想和特征，例如，当理想在它是Fσ或当他们携带一个局部紧群拓扑。我们将这些结果应用于Borel偏序重新推导出一个定理的Todorcevic和Borel等价关系来回答一个问题的Kechris和Louveau。作为另一个应用，我们给出了Cantor集上Maharam子测度μ的μ-零集的σ-理想的一个刻画，这在很大程度上类似于Kechris和作者对微薄理想的刻画。
We study the structure of analytic ideals of subsets of the natural numbers. For example, we prove that for an analytic ideal I, either the ideal {X ⊂ (Ω × Ω: ⊂En X ⊂({0, 1,…,n} × Ω } is Rudin-Keisler below I, or I is very simply induced by a lower semicontinuous submeasure. Also, we show that the class of ideals induced in this manner by lsc submeasures coincides with Polishable ideals as well as analytic P-ideals. We study this class of ideals and characterize, for example, when the ideals in it are Fσ or when they carry a locally compact group topology. We apply these results to Borel partial orders to rederive a theorem of Todorcevic and to Borel equivalence relations to answer a question of Kechris and Louveau. As another application we give a characterization of σ-ideals of μ-zero sets for Maharam submeasures μ on the Cantor set which is to a large extent analogous to a characterization of the meager ideal due to Kechris and the author.