# every ordered field with the least upper bound property is isomorphic to the real numbers

Let $F$ be an ordered field. If $F$ satisfies the least upper bound property
then $F$ is isomorphic^{} as an ordered field to the real numbers $\mathbb{R}$.

Title | every ordered field with the least upper bound property is isomorphic to the real numbers |
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Canonical name | EveryOrderedFieldWithTheLeastUpperBoundPropertyIsIsomorphicToTheRealNumbers |

Date of creation | 2013-03-22 14:10:33 |

Last modified on | 2013-03-22 14:10:33 |

Owner | archibal (4430) |

Last modified by | archibal (4430) |

Numerical id | 4 |

Author | archibal (4430) |

Entry type | Theorem |

Classification | msc 12D99 |

Classification | msc 26-00 |

Classification | msc 54C30 |