Weak prediction principles

Abstract

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 $2^{<\lambda }<2^{\lambda }$ and hence holds at every strongly inaccessible cardinal.

Cited by in corpus (5)

• Negating the Galvin Property
• Cofinal types of ultrafilters over measurable cardinals
• Galvin's property at large cardinals and an application to partition calculus
• Double weakness
• Reflection principles, GCH and the uniformization properties