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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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