# $\mathrm{\u25c7}$ is equivalent to $\mathrm{\u2663}$ and continuum hypothesis

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

$${\mathrm{\u25c7}}_{S}\leftrightarrow {\mathrm{\u2663}}_{S}$$ |

Moreover, this is best possible: $\mathrm{\neg}{\mathrm{\u25c7}}_{S}$ is consistent with ${\mathrm{\u2663}}_{S}$.

Title |
$\mathrm{\u25c7}$ is equivalent^{} to $\mathrm{\u2663}$ and continuum hypothesis^{} |
---|---|

Canonical name | DiamondIsEquivalentToclubsuitAndContinuumHypothesis |

Date of creation | 2013-03-22 12:53:55 |

Last modified on | 2013-03-22 12:53:55 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 6 |

Author | Henry (455) |

Entry type | Theorem |

Classification | msc 03E45 |

Synonym | diamond is equivalent to club and continuum hypothesis |

Related topic | Diamond^{} |

Related topic | Clubsuit |