Cardinal sequences and Cohen real extensions

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 $(2^{\aleph_0})^V$ 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.

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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