I'm wondering if there is a version of Zorn's lemma that applies to collections that are "small" in a sense I'll describe below, and which true independent of the axiom of choice.(adsbygoogle = window.adsbygoogle || []).push({});

Specifically, say I have a collection of sets such that each set in it is countable, but the collection as a whole may be uncountable. I order this collection by inclusion, and show that every chain has an upper bound. I can apply Zorn's lemma and get that there's a maximal element. But what I'm wondering is if I can do this without the usual version Zorn's lemma, which requires the axiom of choice. Every chain must be countable, since otherwise its bound would be uncountable. Is there a way to do this?

**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!

# Zorn's lemma without the axiom of choice

Loading...

Similar Threads - Zorn's lemma without | Date |
---|---|

I Zorn's Lemma | Nov 22, 2016 |

Show that Zorns lemma follows from AC | May 28, 2012 |

What is the simplest proof of Zorn's lemma | Apr 10, 2011 |

Proof of Zorn's Lemma | Nov 8, 2010 |

Zorn's lemma <=> Axiom of choice | Mar 24, 2010 |

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