Relative consistency results via strong compactness

Relative Compactness and Product Stable Quotient Maps

Identity crises and strong compactness

On the Strong Equality between Supercompactness and Strong Compactness

We show that supercompactness and strong compactness can be equivalent even as properties of pairs of regular cardinals. Specifically, we show that if V |= ZFC + GCH is a given model (which in interesting cases contains instances of supercompactness), then there is some cardinal and cofinality preserving generic extension V [G] |= ZFC + GCH in which, (a) (preservation) for κ ≤ λ regular, if V |...

A note on strong compactness and resurrectibility

We construct a model containing a proper class of strongly compact cardinals in which no strongly compact cardinal κ is κ supercompact and in which every strongly compact cardinal has its strong compactness resurrectible.

On Box, Weak Box and Strong Compactness

One of the most important goals of set theorists over the last few years has been to re-prove old results which previously had used very strong assumptions from hypotheses which, at least prima facie, are weaker. Examples of these abound, including, but certainly not limited to, the work of Woodin and Cummings (see [3]) on the Singular Cardinals Problem, in which results previously obtained by ...