Equivalent to the axiom of choice?

Asked Nov 03 '17 at 14:08

Active Jan 10 '18 at 20:50

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Are the two following equivalent under ZF :

Axiom of Choice/Zorn's Lemma
Given any two sets A, B, there exists an injection from A to B or there exists an injection from B to A

I could prove that (1) implies (2) and I wonder if they are actually equivalent but I couldn't prove it. I read somewhere that (2) cannot be proven with only ZF, that's why the equivalence seems plausible to me.

Thank you :)

edited Jan 10 '18 at 20:50

Andrés E. Caicedo

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asked Nov 03 '17 at 14:08

Friedrich

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1

There are probably a few other rogue duplicates, and otherwise related threads. But I'm too lazy to find them now. – Asaf Karagila Nov 03 '17 at 14:18

Equivalent to the axiom of choice?

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