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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On CON($\mathfrak {d}_\lambda >$ cov$_\lambda$(meagre))
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by Saharon Shelah PDF
Trans. Amer. Math. Soc. 373 (2020), 5351-5369 Request permission

Abstract:

We prove the consistency of: for suitable strongly inaccessible cardinal $\lambda$ the dominating number, i.e., the cofinality of ${}^\lambda \lambda$, is strictly bigger than cov$_\lambda$(meagre), i.e., the minimal number of nowhere dense subsets of ${}^\lambda 2$ needed to cover it. This answers a question of Matet.
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Additional Information
  • Saharon Shelah
  • Affiliation: Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel; and Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
  • MR Author ID: 160185
  • ORCID: 0000-0003-0462-3152
  • Email: shelah@math.huji.ac.il
  • Received by editor(s): June 16, 2009
  • Received by editor(s) in revised form: March 30, 2015, November 7, 2017, and July 10, 2019
  • Published electronically: May 28, 2020
  • Additional Notes: This research was supported by the United States-Israel Binational Science Foundation. Publication 945.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 5351-5369
  • MSC (2010): Primary 03E35, 03E55; Secondary 03E17
  • DOI: https://doi.org/10.1090/tran/7948
  • MathSciNet review: 4127879