Cardinal sequences and Cohen real extensions
Tom 181 / 2004
Fundamenta Mathematicae 181 (2004), 75-88
MSC: 54A25, 06E05, 54G12, 03E35.
DOI: 10.4064/fm181-1-3
Streszczenie
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 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.