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Mutual stationarity and singular Jonsson cardinals

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Abstract

We prove that if the sequence \(\langle k_n:1 \le n < \omega\rangle\) contains a so-called gap then the sequence \(\langle S^{\aleph_n}_{\aleph_{k_n}}:1 \le n < \omega\rangle\) of stationary sets is not mutually stationary, provided that \(k_n<n\) for every \(n \in \omega\). We also prove a sufficient condition for being singular Jonsson cardinals.

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Authors and Affiliations

  1. Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    S. Shelah

  2. Department of Mathematics, Hill Center – Busch Campus Rutgers , The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    S. Shelah

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  1. S. Shelah
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Correspondence to S. Shelah.

Additional information

The author thanks Alice Leonhardt for the beautiful typing. References like [5, Th0.2=Ly5] means the label of Th.0.2 is y5. The reader should note that the version in my website is usually more updated than the one in the mathematical archive. This is work 1158 in the author’s list.

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Shelah, S. Mutual stationarity and singular Jonsson cardinals. Acta Math. Hungar. 163, 140–148 (2021). https://doi.org/10.1007/s10474-020-01041-6

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  • DOI: https://doi.org/10.1007/s10474-020-01041-6

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