Finite functions and the necessary use of large cardinals.
Flipping properties and huge cardinals
Flipping properties and supercompact cardinals
Forcing when there are large cardinals: An introduction
Forcing with ideals generated by closed sets
Consider the poset where is an arbitrary -ideal -generated by a projective collection of closed sets. Then the extension is given by a single real of an almost minimal degree: every real is Cohen-generic over or .
Forcings which preserve large cardinals
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.
Free -products of lattices. I
Free -products of lattices. II