Sigma-Prikry forcing, part 2

(joint work with A. Rinot and D. Sinapova)

In the previous talk, we introduced the notion of \Sigma-Prikry forcing and showed that many classical Prikry-type forcing which center on countable cofinalities fall into this framework.

The aim of this talk is to present our iteration scheme for \Sigma-Prikry forcings.

In case time permits, we will also show how to use this general iteration theorem to derive as a corollary the following strengthening of Sharon’s theorem: starting with \omega-many supercompact cardinals one can force a generic extension where Refl(<\omega,\kappa^+) holds and SCH_\kappa fails, for \kappa being a strong limit cardinal with cofinality \omega.

The slides are now available.