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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We introduce a large cardinal property which is consistent with and show that for every superatomic Boolean algebra
and every cardinal
with the large cardinal property, if tightness
, then depth
. This improves a theorem of Dow and Monk.
- [DM] Alan Dow and J. Donald Monk, Depth, 𝜋-character, and tightness in superatomic Boolean algebras, Topology Appl. 75 (1997), no. 2, 183–199. MR 1427748, https://doi.org/10.1016/S0166-8641(96)00088-0
- [J] Thomas Jech, Set theory, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. MR 506523
- [K] J. B. Kruskal, Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s conjecture, Trans. Amer. Math. Soc. 95 (1960), 210–225. MR 111704, https://doi.org/10.1090/S0002-9947-1960-0111704-1
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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