We consider the cardinal sequences of compact scattered spaces in models where CH is false. We describe a number of models of in which no such space can have ℵ₂ countable levels.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-3-4, author = {Kenneth Kunen}, title = {Compact scattered spaces in forcing extensions}, journal = {Fundamenta Mathematicae}, volume = {185}, year = {2005}, pages = {261-266}, zbl = {1083.54023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-3-4} }
Kenneth Kunen. Compact scattered spaces in forcing extensions. Fundamenta Mathematicae, Tome 185 (2005) pp. 261-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-3-4/