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On tightness and depth
in superatomic Boolean algebras


Authors: Saharon Shelah and Otmar Spinas
Journal: Proc. Amer. Math. Soc. 127 (1999), 3475-3480
MSC (1991): Primary 06E05
DOI: https://doi.org/10.1090/S0002-9939-99-04944-8
Published electronically: May 13, 1999
MathSciNet review: 1610793
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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a large cardinal property which is consistent with $L$ and show that for every superatomic Boolean algebra $B$ and every cardinal $\lambda $ with the large cardinal property, if tightness$^{+}(B)\geq \lambda ^{+}$, then depth$(B)\geq \lambda $. This improves a theorem of Dow and Monk.


References [Enhancements On Off] (What's this?)

  • [DM] A. Dow and D. Monk, Depth, $\pi $-character, and tightness in superatomic Boolean algebras, Top. and its Appl. 75(1997), 183-199. MR 98a:54002
  • [J] T. Jech, Set Theory, Academic Press, New York, 1978. MR 80a:03062
  • [K] J. Kruskal, Well-quasi ordering, the tree theorem and Vazsonyi's conjecture, Trans. Am. Math. Soc. 95(1960), 210-225. MR 22:2566

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Additional Information

Saharon Shelah
Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel
Email: shelah@math.huji.ac.il

Otmar Spinas
Affiliation: Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
Email: spinas@math.ethz.ch

DOI: https://doi.org/10.1090/S0002-9939-99-04944-8
Received by editor(s): November 18, 1997
Received by editor(s) in revised form: February 13, 1998
Published electronically: May 13, 1999
Additional Notes: The first author was supported by the Basic Research Foundation of the Israel Academy of Sciences; publication 663.
The second author was partially supported by the Alexander von Humboldt Foundation and grant 2124-045702.95/1 of the Swiss National Science Foundation.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 1999 American Mathematical Society

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