Set Theory and Applications

这个项目将集中于集合论和集合论在代数中的应用。主要研究课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性理论、可数完全滤波器和理想、无穷组合学和布尔代数问题。拟议的研究涉及被称为集合论的抽象数学学科。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。它对抽象无限集的研究提供了对现代数学表达能力及其局限性的宝贵见解。特别是强调独立性证明和大基数理论的现代集合论，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。

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.