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/