Hybrid Prikry forcing
Tom 228 / 2015
Fundamenta Mathematicae 228 (2015), 139-152 MSC: 03E04, 03E35, 03E55. DOI: 10.4064/fm228-2-2
We present a new forcing notion combining diagonal supercompact Prikry forcing with interleaved extender based forcing. We start with a supercompact cardinal $\kappa $. In the final model the cofinality of $\kappa $ is $\omega $, the singular cardinal hypothesis fails at $\kappa $, and GCH holds below $\kappa $. Moreover we define a scale at $\kappa $ which has a stationary set of bad points in the ground model.