Combinatorics on medium-sized infinite cardinals

大于等于aleph 2的无穷基数的组合学呈现出与aleph 1不同的方面，即最小不可数基数。本文从相对较小的无穷基数与集合论中几个著名公理的相互作用以及对集合论拓扑的影响两个方面，研究了大于等于aleph 2的无穷基数的内在组合性质，得到了这方面的几个有意义的结果。

Combinatorics of infinite cardinals greater than or equal to aleph 2 take on a different aspect from that of aleph 1, that is, the least uncountable cardinal. In this research, we studied inherent combinatorial nature of relatively small infinite cardinals greater than or equal to aleph 2, from the aspect of its interaction with several well-known axioms of set theory and that of its influence on set-theoretic topology, and obtained several significant results in this area.