Cardinal sequences and Cohen real extensions

István Juhász; Saharon Shelah; Lajos Soukup; Zoltán Szentmiklóssy

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Cardinal sequences and Cohen real extensions

István Juhász·Saharon Shelah·Lajos Soukup·Zoltán Szentmiklóssy

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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 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.

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BibTeX RIS

István Juhász, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy. 2004-04-19. Cardinal sequences and Cohen real extensions. https://arxiv.org/abs/math/0404322

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