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/