On diamond sequences
Large cardinals and covering numbers
The paper is concerned with the computation of covering numbers in the presence of large cardinals. In particular, we revisit Solovay's result that the Singular Cardinal Hypothesis holds above a strongly compact cardinal.
The covering number for category and partition relations on
We show that cov(M) is the least infinite cardinal λ such that (the set of all finite subsets of λ ) fails to satisfy a certain natural generalization of Ramsey’s Theorem.
Normal restrictions of the noncofinal ideal on
We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.
Club-guessing, good points and diamond
Shelah’s club-guessing and good points are used to show that the two-cardinal diamond principle holds for various values of and .
Fragments of strong compactness, families of partitions and ideal extensions
We investigate some natural combinatorial principles related to the notion of mild ineffability, and use them to obtain new characterizations of mild ineffable and weakly compact cardinals. We also show that one of these principles may be satisfied by a successor cardinal. Finally, we establish a version for of the canonical Ramsey theorem for pairs.
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