# complete partial orders do not add small subsets

Suppose $P$ is a $\mathrm{\xce\u0219}$-complete partial order in $\mathrm{\u0111\x9d\x94\x90}$. Then for any generic subset $G$, $\mathrm{\u0111\x9d\x94\x90}$ contains no bounded subsets of $\mathrm{\xce\u0219}$ which are not in $\mathrm{\u0111\x9d\x94\x90}$.

Title | complete partial orders do not add small subsets |
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Canonical name | CompletePartialOrdersDoNotAddSmallSubsets |

Date of creation | 2013-03-22 12:53:32 |

Last modified on | 2013-03-22 12:53:32 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 4 |

Author | Henry (455) |

Entry type | Theorem |

Classification | msc 03E40 |