Set Theory and Applications

集合论及其应用

• 批准号: 9802783
• 负责人: Thomas Jech
• 金额: $ 6.86万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802783&HistoricalAwards=false
• 关键词: Set; Theory; Applications

This project will concentrate on set theory and applications of set theory in algebra. The major topics of research will include left-distributive algebras, elementary embeddings, stationary sets, the theory of large cardinals, applications of forcing, the singular cardinals problem and the theory of possible cofinalities, countably complete filters and ideals, infinitary combinatorics, and problems in Boolean algebras.The proposed research deals with the abstract mathematical discipline called set theory. Set theory serves as the foundation for other mathematical disciplines such as topology, measure theory, and functional analysis. Its study of abstract infinite sets provides an invaluable insight into the expressive power of modern mathematics and its limitations. In particular, modern set theory with its emphasis on independence proofs and the theory of large cardinals enables to establish provability or unprovability and analyze the complexity of mathematical conjectures.

该项目将集中于集合论以及集合论在代数中的应用。研究的主要主题将包括左分配代数、初等嵌入、平稳集、大基数理论、强迫的应用、奇异基数问题和可能共尾性理论、可数完备滤波器和理想、无限组合以及布尔代数问题。拟议的研究涉及称为集合论的抽象数学学科。集合论是拓扑学、测度论和泛函分析等其他数学学科的基础。它对抽象无限集的研究为现代数学的表达能力及其局限性提供了宝贵的见解。特别是，现代集合论强调独立性证明和大基数理论，能够建立可证明性或不可证明性，并分析数学猜想的复杂性。