Fragments of strong compactness, families of partitions and ideal extensions
Volume 234 / 2016
Fundamenta Mathematicae 234 (2016), 171-190
MSC: Primary 03E55, 03E02; Secondary 03E05.
DOI: 10.4064/fm172-1-2016
Published online: 9 March 2016
Abstract
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 $\mathcal {P}_\kappa (\lambda )$ of the canonical Ramsey theorem for pairs.
