Weak prediction principles

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Abstract

We prove the consistency of the failure of the weak diamond Φ λ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond Ψ λ is equivalent to the statement 2 < 2 λ and hence holds at every strongly inaccessible cardinal.

Original languageAmerican English
Pages (from-to)109-125
Number of pages17
JournalFundamenta Mathematicae
Volume245
Issue number2
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN

Keywords

  • Radin forcing
  • Very weak diamond
  • Weak diamond

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