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In The Man Who Loved Only Numbers, a biography about Paul Erdős, by Paul Hoffman, the author claims that Paul Cohen was "Gödel's former assistant" (p 225). However, I can't find any other sources corroborating the claim, and while I don't know much about either of them, I was under the impression that Cohen's main work before his work on the Continuum Hypothesis was in analysis, and that his achievements in logic were especially impressive because he didn't have much prior experience in the field.

According to wikipedia, Cohen was "a fellow at the Institute for Advanced Study at Princeton [from 1959-61]", during which time Gödel was also there, so it's conceivable that they could have met, but it still seems surprising that he would have taken an analyst as his assistant. Are there any other sources that make this claim?

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  • $\begingroup$ There is no such info in : Akihiro Kanamori, Cohen and Set Theory, BSL (2008). Only : "Cohen spent the years 1959-1961 at the Institute for Advanced Study at Princeton as a fellow and then became an assistant professor at Stanford University." $\endgroup$ – Mauro ALLEGRANZA May 14 '18 at 19:05
  • $\begingroup$ @MauroALLEGRANZA Thanks, that's probably as close to a definitive answer as possible, especially since page 361 describes the men meeting and makes no mention of the supposed "assistantship". If my suspicion is correct, the answer is negative, and will be difficult to disprove, so you could post this as answer and I could wait a day or two to see if anyone else has evidence of this before accepting. $\endgroup$ – Kevin Long May 14 '18 at 19:18
  • $\begingroup$ "Assistant" is not "student". Members of IAS, who have no teaching duties, sometimes would recruit young Ph.D.s to act as their "assistant". For example, Einstein would have mathematicians or physicists as assistant, one after the other. I don't know whether Gödel did this or not. Two of Einstein's assistants are mentioned here: en.wikipedia.org/wiki/Albert_Einstein $\endgroup$ – Gerald Edgar May 14 '18 at 20:26
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No, he was not. Cohen wrote his own account of the history of forcing, The Discovery of Forcing (Rocky Mountain J. Math. 32 (4) (2002), 1071-1100), where he addresses his relationship with Gödel in detail. In particular, he calls him "one of my heroes" (along with Skolem), and mentions some conversations "years later, after my own proof". Nonetheless, it ends with the following:

"Finally a personal remark. I cannot say that I was a friend of Kurt Gödel. We met relatively few times and there was a gulf of age and background that I found difficult to bridge. Yet, my meetings with him were charged with an emotion that was intense, yet difficult to describe. We each traversed journeys that had much in common. I would like to dedicate this talk to his memory."

Cohen was self-taught as a logician. His interest in independence came from discussions on foundations of mathematics with Feferman and Royden at Stanford in 1962. At some point he came to read "Gödel's monograph" The Consistency of the Continuum Hypothesis, actually a compilation of lecture notes for a course given at the Institute for Advanced Study in 1938-39 (Cohen was there in 1959-61). He was even unaware of Shepherdson's follow-up work which showed that inner models could not prove the consistency of the negation of AC or CH, something he rediscovered in 1962.

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