# equivalence of forcing notions

Let $P$ and $Q$ be two forcing^{} notions such that given any generic^{} subset $G$ of $P$ there is a generic subset $H$ of $Q$ with $\U0001d510[G]=\U0001d510[H]$ and vice-versa. Then $P$ and $Q$ are equivalent^{}.

Since if $G\in \U0001d510[H]$, $\tau [G]\in \U0001d510$ for any $P$-name $\tau $, it follows that if $G\in \U0001d510[H]$ and $H\in \U0001d510[G]$ then $\U0001d510[G]=\U0001d510[H]$.

Title | equivalence of forcing notions |
---|---|

Canonical name | EquivalenceOfForcingNotions |

Date of creation | 2013-03-22 12:54:24 |

Last modified on | 2013-03-22 12:54:24 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 5 |

Author | Henry (455) |

Entry type | Definition |

Classification | msc 03E35 |

Classification | msc 03E40 |

Synonym | equivalent |

Related topic | Forcing |

Related topic | ProofThatForcingNotionsAreEquivalentToTheirComposition |