### 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
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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