Double weakness


We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal \(\lambda\) for which the sequence \(\langle 2^\theta:\theta<\lambda\rangle\) is not eventually constant and the weak diamond fails at \(\lambda\). We also prove that consistently diamond fails but a parametrized version of weak diamond holds at some strongly inaccessible \(\lambda\).

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Corresponding author

Correspondence to S. Garti.

Additional information

Both authors are grateful to the generous support of the European Research Council, grant no. 338821. This is publication 1111 of the second author.

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Garti, S., Shelah, S. Double weakness. Acta Math. Hungar. (2021).

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Key words and phrases

  • weak diamond
  • very weak diamond
  • weakly inaccessible
  • Cohen forcing
  • Radin forcing

Mathematics Subject Classification

  • 03E35