Cardinal sequences and Cohen real extensions

István Juhász, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy

Published 2004-04-19Version 1

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.