Mathematical Sciences: Descriptive Set Theory

描述集合论是数理逻辑的分支 关于实数的可定义集合。 研究涉及 描述集合论中的几个主题 描述性集合论和数学的其他部分之间的联系， 特别是分析和拓扑学。 其中一些主题将是 在各种类型的确定性假设下考虑。 一个 项目概要如下。 1. 经典描述集合论及其与 分析和拓扑。 1.1射影层次中点集的分类。 1.2描述性集合论现象的例子发生在 分析和拓扑。 1.3描述集合论与泛函分析：序列 在Banach空间中。 1.4描述集合论与拓扑学：路径，路径- 连通性和简单连通性。 2. 现代描述集合论及其与其他 部分数学逻辑。 2.1阴谋集团宇宙中的集合论 2.2阴谋集团宇宙中的描述性集合论。 2.3跳转操作符和内部模型操作符。

Descriptive set theory is the branch of mathematical logic concerned with definable sets of reals. The research involves several topics in descriptive set theory and in the relationship between descriptive set theory and other parts of mathematics, particularly analysis and topology. Some of these topics will be considered under various types of determinacy assumptions. An outline of the project follows. 1. Classical descriptive set theory and its connections with analysis and topology. 1.1 Classification of pointsets in the projective hierarchy. 1.2 Examples of descriptive set theoretic phenomena occurring in analysis and topology. 1.3 Descriptive set theory and functional analysis: Sequences in Banach spaces. 1.4 Descriptive set theory and topology: Paths, path- connectedness and simple connectedness. 2. Modern descriptive set theory and its connections with other parts of mathematical logic. 2.1 Set theory in the Cabal universe. 2.2 Descriptive set theory in Cabal universe. 2.3 Jump operators and inner model operators.