Combinatorial set theory

该提案的主要重点是使用一系列数学工具对几种类型的无限结构进行调查。第二个重点是研究使用某些无限“极限”结构的超大型有限结构的问题。其中一些问题是“试题”，旨在促进新思想和新方法的发展。提案的主题主要涉及大型基数、ZFC组合学(特别是奇异基数)和强迫。它们包括奇点继承者的强迫公理、树性质的各种形式、紧性性质之间的联系、PCF理论和普适数。提案的最后一部分是关于Razborov的旗代数理论中出现的问题。

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.