Starting from large cardinals we construct a pair V₁⊆ V₂ of models of ZFC with the same cardinals and cofinalities such that GCH holds in V₁ and fails everywhere in V₂.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-2-3,
author = {Sy-David Friedman and Mohammad Golshani},
title = {Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {171-193},
zbl = {1330.03083},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-2-3}
}
Sy-David Friedman; Mohammad Golshani. Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH. Fundamenta Mathematicae, Tome 220 (2013) pp. 171-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-2-3/