A tall space with a small bottom
HTML articles powered by AMS MathViewer
- by István Juhász, Saharon Shelah, Lajos Soukup and Zoltán Szentmiklóssy PDF
- Proc. Amer. Math. Soc. 131 (2003), 1907-1916 Request permission
Abstract:
We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if $\kappa ^{<\kappa } = \kappa$, then there is such a space of height $\kappa ^+$ with only $\kappa$ many isolated points. This implies that there is a locally compact scattered space of height ${\omega }_2$ with $\omega _1$ isolated points in ZFC, solving an old problem of the first author.References
- James E. Baumgartner and Saharon Shelah, Remarks on superatomic Boolean algebras, Ann. Pure Appl. Logic 33 (1987), no. 2, 109–129. MR 874021, DOI 10.1016/0168-0072(87)90077-7
- I. Juhász and W. Weiss, On thin-tall scattered spaces, Colloq. Math. 40 (1978/79), no. 1, 63–68. MR 529798, DOI 10.4064/cm-40-1-63-68
- Winfried Just, Two consistency results concerning thin-tall Boolean algebras, Algebra Universalis 20 (1985), no. 2, 135–142. MR 806609, DOI 10.1007/BF01278592
- Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
- Juan Carlos Martínez, A forcing construction of thin-tall Boolean algebras, Fund. Math. 159 (1999), no. 2, 99–113. MR 1670099, DOI 10.4064/fm-159-2-99-113
- Judy Roitman, Height and width of superatomic Boolean algebras, Proc. Amer. Math. Soc. 94 (1985), no. 1, 9–14. MR 781045, DOI 10.1090/S0002-9939-1985-0781045-0
- Saharon Shelah, On what I do not understand (and have something to say). I, Fund. Math. 166 (2000), no. 1-2, 1–82. Saharon Shelah’s anniversary issue. MR 1804704, DOI 10.4064/fm-166-1-2-1-82
Additional Information
- István Juhász
- Affiliation: Alfréd Rényi Institute of Mathematics, P.O. Box 127, 1364 Budapest, Hungary
- Email: juhasz@renyi.hu
- Saharon Shelah
- Affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
- Lajos Soukup
- Affiliation: Alfréd Rényi Institute of Mathematics, P.O. Box 127, Budapest, Hungary
- Email: soukup@renyi.hu
- Zoltán Szentmiklóssy
- Affiliation: Eötvös University of Budapest, 1117, Budapest, Pázmány Péter Sétány 1/C, Hungary
- Email: zoli@renyi.hu
- Received by editor(s): April 4, 2001
- Received by editor(s) in revised form: December 4, 2001
- Published electronically: January 2, 2003
- Additional Notes: The first, third and fourth authors were supported by the Hungarian National Foundation for Scientific Research grant no. 25745
The second author was supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. Publication 714
The third author was partially supported by Grant-in-Aid for JSPS Fellows No. 98259 of the Ministry of Education, Science, Sports and Culture, Japan - Communicated by: Alan Dow
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1907-1916
- MSC (2000): Primary 54A25, 06E05, 54G12, 03E20
- DOI: https://doi.org/10.1090/S0002-9939-03-06662-0
- MathSciNet review: 1955280