Cardinal sequences and Cohen real extensions

• Autorzy: István Juhász , Saharon Shelah , Lajos Soukup , Zoltán Szentmiklóssy
• Języki publikacji: EN

Abstrakty

EN

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 $(2^{ℵ₀})^V$ levels of size ω. 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.

Kategorie tematyczne

• 06E05: Structure theory
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54G12: Scattered spaces
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 1
• Strony: 75-88

Daty

wydano

2004

Twórcy

autor

István Juhász

• Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, H-1053 Budapest, Hungary

autor

Saharon Shelah

• Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel

autor

Lajos Soukup

• Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, H-1053 Budapest, Hungary

autor

Zoltán Szentmiklóssy

• Department of Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/fm181-1-3