Set Theory and Applications

这个项目将集中在集合论和集合论在代数中的应用。主要研究课题包括左分配代数、初等嵌入、固定集合、大基数理论、强迫的应用、奇异基数问题和可能的共尾性理论、可数完备滤子和理想、无穷组合学以及布尔代数问题。拟议研究涉及抽象数学学科集合论。集合论是其他数学学科的基础，如拓扑学、测度论和泛函分析。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，使建立可证明性或不可证明性和分析数学命题的复杂性。

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.