Given the theory $$ \operatorname{ZF} + \text{For every graph G, if every finite subgraph is 3-colorable, then G is 3-colorable} $$ How can I prove the Boolean Prime Ideal Theorem?

(This is problem 2.24 in Jech's book "The Axiom of Choice")

  • $\begingroup$ You're right. Sorry 'bout that. Did you follow the references in the historical notes? $\endgroup$ – Asaf Karagila Dec 3 '16 at 18:17

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