Mathematical Sciences: Set Theory

数学科学：集合论

• 批准号: 9401275
• 负责人: Thomas Jech
• 金额: $ 12.35万
• 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: 1994
• 资助国家: 美国
• 起止时间: 1994-10-15 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401275&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Set; Theory

9401275 Jech This research project will concentrate on set theory and on 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. This 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 one to establish provability or unprovability and analyze the complexity of mathematical conjectures. ***

小行星9401275 这个研究项目将集中在集合论和集合论在代数中的应用。 主要的研究课题将包括左分配代数，初等嵌入，固定集，大基数理论，强制应用，奇异基数问题和可能的共尾性理论，可数完全过滤器和理想，无限组合学和布尔代数问题。 这项研究涉及抽象的数学学科称为集合论。 集合论是其他数学学科如拓扑学、测度论和泛函分析的基础。 它对抽象无限集合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，它强调独立性证明和大基数理论，使人们能够建立可证明性或不可证明性，并分析数学命题的复杂性。 ***