Cardinal sequences and Cohen real extensions
Volume 181 / 2004
Fundamenta Mathematicae 181 (2004), 75-88
MSC: 54A25, 06E05, 54G12, 03E35.
DOI: 10.4064/fm181-1-3
Abstract
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 $(2^{\aleph_0})^V$ levels of size $\omega$. We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of regular and of $0$-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.
