Double weakness

Abstract

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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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). https://doi.org/10.1007/s10474-021-01132-y

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Key words and phrases

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

Mathematics Subject Classification

  • 03E35