Notes on singular cardinal combinatorics (Q816288)

This paper, an extended version of the author's 2004 Banff lectures, contains a lovely compendium of combinatorial results on successors of singular cardinals, from various authors. The following are the key words on the theorems which are proved, in most cases completely, in an informal style. GCH implies diamond. Club guessing holds in ZFC. Square implies the existence of Souslin tree. Weak square is equivalent to the existence of a special tree. There is a stationary set with square on it. Properties of Shelah's \(I[\lambda]\). Internally approaching chains. Scales, good points, essential upper bounds. Incompactness of systems of countable sets with transversals. Good scales. Various forms of the square principle are negated by PFA, MM. Shelah's trichotomy theorem, very good scales if SCH fails.