We show that if we add any number of Cohen reals to the ground model then, in the generic extension, a locally compact scattered space has at most levels of size ω. We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of regular and of 0-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-1-3,
author = {Istv\'an Juh\'asz and Saharon Shelah and Lajos Soukup and Zolt\'an Szentmikl\'ossy},
title = {Cardinal sequences and Cohen real extensions},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {75-88},
zbl = {1052.54004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-1-3}
}
István Juhász; Saharon Shelah; Lajos Soukup; Zoltán Szentmiklóssy. Cardinal sequences and Cohen real extensions. Fundamenta Mathematicae, Tome 184 (2004) pp. 75-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-1-3/