Some applications of combinatorics in descriptive set theory.

机译：组合语在描述集理论中的一些应用。

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We investigate the relationship between classical combinatorics and descriptive set theory. Establishing new results in the areas of intersecting families and partitions of the complete binary tree, we subsequently analyze ramifications in the study of Borel equivalence relations and canonization theorems on Cantor space. We also examine metric space valued random variables as well as finite measure spaces. In all of these inquiries we employ the same basic strategy: approximate the object in question by combinatorially simple structures, and analyze how the combinatorics of the approximations yield desired information.

机译：我们研究了经典组合学与描述性集合论之间的关系。在完整二叉树的相交族和分区的区域中建立新结果后，我们随后在Cantor空间上的Borel等价关系和正则定理的研究中分析了分支。我们还将检查度量空间值随机变量以及有限度量空间。在所有这些查询中，我们都采用相同的基本策略：通过组合简单的结构对有问题的对象进行近似，并分析近似的组合如何产生所需的信息。

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作者
Conley, Clinton Taylor.;
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作者单位

University of California, Los Angeles.;

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授予单位 University of California, Los Angeles.;
学科 Mathematics.
学位 Ph.D.
年度 2009
页码 85 p.
总页数 85
原文格式 PDF
正文语种 eng
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入库时间 2022-08-17 11:38:19

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Some applications of combinatorics in descriptive set theory.

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