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

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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 $\clubsuit_{S}$ .

Synonym:

diamond is equivalent to club and continuum hypothesis

Type of Math Object:

Theorem

Major Section:

Reference

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