Mutual stationarity and singular Jonsson cardinals

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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Correspondence to S. Shelah.

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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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Key words and phrases

  • combinatorial set theory
  • Jonsson cardinal
  • mutual stationarity

Mathematics Subject Classification

  • primary 03E55
  • secondary 03E40