Weak prediction principles
Volume 245 / 2019
Fundamenta Mathematicae 245 (2019), 109-125
MSC: Primary 03E05, 03E55.
DOI: 10.4064/fm576-6-2018
Published online: 2 January 2019
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^{ \lt \lambda } \lt 2^\lambda $ and hence holds at every strongly inaccessible cardinal.
