Geodesic
Cardinal sequences and Cohen real extensions
István Juhász1 ; Saharon Shelah2 ; Lajos Soukup1 ; Zoltán Szentmiklóssy3
1 Alfréd Rényi Institute of Mathematics Reáltanoda u. 13–15 H-1053 Budapest, Hungary
2 Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem, Israel
3 Department of Analysis Eötvös Loránd University Pázmány Péter sétány 1/c H-1117 Budapest, Hungary
Fundamenta Mathematicae, Tome 181 (2004) no. 1, pp. 75-88.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm181-1-3
Keywords: number cohen reals ground model generic extension locally compact scattered space has aleph levels size omega complete zfc characterization cardinal sequences regular scattered spaces although classes regular dimensional scattered spaces different prove have cardinal sequences

István Juhász 1 ; Saharon Shelah 2 ; Lajos Soukup 1 ; Zoltán Szentmiklóssy 3

1 Alfréd Rényi Institute of Mathematics Reáltanoda u. 13–15 H-1053 Budapest, Hungary
2 Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem, Israel
3 Department of Analysis Eötvös Loránd University Pázmány Péter sétány 1/c H-1117 Budapest, Hungary 
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István Juhász; Saharon Shelah; Lajos Soukup; Zoltán Szentmiklóssy. Cardinal sequences and Cohen real extensions. Fundamenta Mathematicae, Tome 181 (2004) no. 1, pp. 75-88. doi : 10.4064/fm181-1-3. http://geodesic.mathdoc.fr/articles/10.4064/fm181-1-3/

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