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Weak prediction principles

Volume 245 / 2019

Omer Ben-Neria, Shimon Garti, Yair Hayut Fundamenta Mathematicae 245 (2019), 109-125 MSC: Primary 03E05, 03E55. DOI: 10.4064/fm576-6-2018 Published online: 2 January 2019


We prove the consistency of the failure of the weak diamond $\Phi _\lambda $ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond $\Psi _\lambda $ is equivalent to the statement $2^{ \lt \lambda } \lt 2^\lambda $ and hence holds at every strongly inaccessible cardinal.


  • Omer Ben-NeriaDepartment of Mathematics
    University of California, Los Angeles
    Los Angeles, CA 90095-1555, U.S.A.
  • Shimon GartiInstitute of Mathematics
    The Hebrew University of Jerusalem
    Jerusalem 91904, Israel
  • Yair HayutSchool of Mathematical Sciences
    Tel Aviv University
    Tel Aviv 69978, Israel

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