### 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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