Combinatorial set theory

该提案的主要重点是使用一系列数学工具调查几种类型的无限结构。第二个重点是调查的问题，非常大的有限结构，使用某些无限的“限制”结构。有些问题是“测试题”，旨在促进新思想和新方法的发展。建议的主题主要涉及大基数，ZFC组合学（特别是奇异基数）和强迫。它们包括奇点后继的强迫公理，树性质的各种形式，紧性之间的联系，PCF理论和普适数。最后一节的建议是有关的问题所产生的拉兹博罗夫理论的旗帜代数。

The main focus of the proposal is the investigation of several types of infinite structure, using a range of mathematical tools. A secondary focus is the investigation of problems about very large finite structures, using certain infinite "limit" structures. Some of the problems to be studied are "test questions" intended to stimulate the development of new idea and methods.The topics of the proposal are mostly concerned with large cardinals, ZFC combinatorics (particularly of singular cardinals) and forcing. They include forcing axioms for successors of singulars, various forms of the tree property, connections between compactness properties, PCF theory and universality numbers. The last section of the proposal is concerned with problems arising in Razborov's theory of flag algebras.