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Transactions of the American Mathematical Society

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On CON($\mathfrak {d}_\lambda >$ cov$_\lambda$(meagre))


Author: Saharon Shelah
Journal: Trans. Amer. Math. Soc. 373 (2020), 5351-5369
MSC (2010): Primary 03E35, 03E55; Secondary 03E17
DOI: https://doi.org/10.1090/tran/7948
Published electronically: May 28, 2020
MathSciNet review: 4127879
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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

Keywords: Set theory, independence, forcing, cardinal invariants, inaccessible
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.
Article copyright: © Copyright 2020 American Mathematical Society