English

Weak prediction principles

Logic 2019-03-12 v2

Abstract

We prove the consistency of the failure of the weak diamond Φλ\Phi_\lambda at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond Ψλ\Psi_\lambda is equivalent to the statement 2<λ<2λ2^{<\lambda}<2^\lambda and hence holds at every strongly inaccessible cardinal.

Keywords

Cite

@article{arxiv.1610.08620,
  title  = {Weak prediction principles},
  author = {Omer Ben-Neria and Shimon Garti and Yair Hayut},
  journal= {arXiv preprint arXiv:1610.08620},
  year   = {2019}
}