Semigroups of Mappings: Set Theoretic, Analytic, and Combinatorial Aspects

这个项目的目的是研究各种自然半群的相对秩与某些小基数不变量之间的联系，例如Cichon图中的基数不变量。半群S的子半群T的相对秩是S的一个子集的最小基数，该子集与T一起生成整个S。因此，相对秩可以被看作是经典秩概念的无限模拟，即生成元的最少数量。研究人员建议与Cichon和Morayne教授（弗罗茨瓦夫理工大学，波兰）合作进行这项研究。为主要调查员前往波兰进行四次访问以开展合作研究，寻求旅费和生活费方面的支助。该项目结合了拓扑学、代数学、组合学和集合论。研究人员和教授Cichon和Morayne的综合专业知识涵盖了这些研究领域。

The aim of this project is to investigate the connections between relative ranks of various natural semigroups and certain small cardinal invariants, such as those in Cichon's diagram. The relative rank of a subsemigroup T of a semigroup S is the least cardinal of a subset of S that together with T generates the whole of S. As such, relative ranks can be seen as an infinite analogue of the classical notion of rank, i.e. the least number of generators. The investigators propose to perform this research in collaboration with Professors Cichon and Morayne (Wroclaw University of Technology, Poland). Support is sought for travel and subsistence for the principal investigator to make four visits to Poland, to carry out collaborative research. The proposed project combines aspects of topology, algebra, combinatorics, and set theory. The combined expertise of the investigator and Professors Cichon and Morayne encompasses these fields of research.