István Juhász, Saharon Shelah, Lajos Soukup and Zoltán Szentmiklóssy
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 many levels of size .
We also give a complete 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.
Key words and phrases: locally compact scattered space, superatomic Boolean algebra, Cohen reals, cardinal sequence, regular space, 0-dimensional
2000 Mathematics Subject Classification: 54A25, 06E05, 54G12, 03E35
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