# $\Diamond$ is equivalent to $\clubsuit$ and continuum hypothesis

If $S$ is a stationary subset of $\kappa$ and $\lambda<\kappa$ implies $2^{\lambda}\leq\kappa$ then

 $\Diamond_{S}\leftrightarrow\clubsuit_{S}$

Moreover, this is best possible: $\neg\Diamond_{S}$ is consistent with $\clubsuit_{S}$.

Title $\Diamond$ is equivalent to $\clubsuit$ and continuum hypothesis DiamondIsEquivalentToclubsuitAndContinuumHypothesis 2013-03-22 12:53:55 2013-03-22 12:53:55 Henry (455) Henry (455) 6 Henry (455) Theorem msc 03E45 diamond is equivalent to club and continuum hypothesis Diamond Clubsuit