On tightness and depth in superatomic Boolean algebras
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- by Saharon Shelah and Otmar Spinas PDF
- Proc. Amer. Math. Soc. 127 (1999), 3475-3480 Request permission
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
- Alan Dow and J. Donald Monk, Depth, $\pi$-character, and tightness in superatomic Boolean algebras, Topology Appl. 75 (1997), no. 2, 183–199. MR 1427748, DOI 10.1016/S0166-8641(96)00088-0
- Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
- J. B. Kruskal, Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s conjecture, Trans. Amer. Math. Soc. 95 (1960), 210–225. MR 111704, DOI 10.1090/S0002-9947-1960-0111704-1
Additional Information
- Saharon Shelah
- Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
- Otmar Spinas
- Affiliation: Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
- Email: spinas@math.ethz.ch
- 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.
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3475-3480
- MSC (1991): Primary 06E05
- DOI: https://doi.org/10.1090/S0002-9939-99-04944-8
- MathSciNet review: 1610793