Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I know that the law of the excluded middle is implied in ZFC set theory, since it is implied by the axiom of choice. Taking away the axiom of choice, does ZF set theory (with axioms as stated in the Wikipedia article http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory), imply the law of the excluded middle [for infinite sets]?

If LEM does follow from ZF, could you please provide the proof if you know it, or point me to the proof if you know where it is, or tell me what ZF axioms it follows from if you don't know of theproof or its location?

Thanks very much.

-HJ Farnsworth

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# ZF Set Theory and Law of the Excluded Middle

Loading...

Similar Threads - Theory Excluded Middle | Date |
---|---|

I Countability of ℚ | Feb 12, 2018 |

A Is there a decidable set theory? | Feb 8, 2018 |

About the strategy of reducing the total suffering in a queue | Dec 28, 2017 |

B Empty domains and the vacuous truth | Dec 26, 2017 |

Excluded middle and self-reference | Apr 27, 2013 |

**Physics Forums - The Fusion of Science and Community**