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The wikipedia article on Paul Cohen mentions that:

Cohen is noted for developing a mathematical technique called forcing, which he used to prove that neither the continuum hypothesis (CH), nor the axiom of choice, can be proved from the standard Zermelo–Fraenkel axioms (ZF) of set theory.

I am trying to find out the exact year in which Coehn first proved the result concerning the axiom of choice and the year and the paper when it was first published, if ever. All I have found are two papers related to this. (See here and here.) However both of these relate to the independence of the continuum hypothesis and not of the axiom of choice. My precise questions are in which year did Cohen prove the result concerning the axiom of choice, and when was it first published or presented?

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Aki Kanamori discusses the history in great detail in this address; the first paper containing the result was called Independence of the Axiom of Choice and was circulated at Stanford in 1963 but not published. It is cited in his book Set Theory and the Continuum Hypothesis, however. The two PNAS papers, despite their titles, contain the first published version.

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But not the proof, actually. –  Asaf Karagila Sep 20 '12 at 6:10
    
@Asaf, I was hoping you would show up here. So, is it really true that Cohen's first publication of the proof of the independence of AC, not counting unpublished notes circulating informally, was in that 1966 book Brian cites? –  Gerry Myerson Sep 21 '12 at 0:31
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http://plato.stanford.edu/entries/axiom-choice/ says it was 1963 and cites Cohen, P.J., 1963. “The independence of the continuum hypothesis I,” Proceedings of the U.S. National Academy of Sciemces, 50: 1143–48. I think you'll find AC and CH were done together.

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That is the paper I have linked in my post above. As you can see it (by clicking on the link) it is concerning the independence of CH. I am not sure that both CH and AC are done together because I cannot understand the proof. –  Shahab Sep 20 '12 at 5:24
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Part of Theorem 1 on the first page of the first paper says that there are models of ZF in which AC holds, and models in which AC fails. But then he says he doesn't prove that part of Theorem 1, so I'm not sure what's going on. –  Gerry Myerson Sep 20 '12 at 5:57
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