Cardinal sequences and Cohen real extensions

by Juhasz and Shelah and Soukup and Szentmiklossy. [JShSS:765]
Fundamenta Math, 2004
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 (2^{aleph_0})^V many levels of size omega . We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of the regular and of the 0-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.

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