We present a new forcing notion combining diagonal supercompact Prikry forcing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ, and GCH holds below κ. Moreover we define a scale at κ which has a stationary set of bad points in the ground model.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-2-2,
author = {Dima Sinapova},
title = {Hybrid Prikry forcing},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {139-152},
zbl = {06390216},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-2-2}
}
Dima Sinapova. Hybrid Prikry forcing. Fundamenta Mathematicae, Tome 228 (2015) pp. 139-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-2-2/