Odifreddi doesn't give a cite (at least in proposition XI.2.10) for the proposition that every non-zero r.e. degree computes a 1-generic. What paper should I cite for this proposition?
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1$\begingroup$ The result can be also found in Soare's old version (Ex 3.9, page 99). The proof is credited to Shore. But I remember Shore told me he just found a non-full approximation proof that is not the the first one. I could not find his email right now. But I remember he told who proved it first. $\endgroup$– 喻 良Commented Nov 1, 2022 at 1:08
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$\begingroup$ I'll email him and ask him. $\endgroup$– Peter GerdesCommented Nov 4, 2022 at 18:16
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For the benefit of others, I emailed Shore and asked him about it and he told me that while he had assumed when he proved it that it wasn't a novel result he never actually found any earlier proof (much less a publication). So, absent contrary evidence turning up I think it's Shore who should get the citation for the claim. I've reproduced the citation he gave me from his email.
The Turing Degrees: An Introduction, in Forcing, Iterated Ultrapowers, and Turing Degrees, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 29, eds. Chong Chi Tat, Feng Qi, Yang Yue, Theodore Slaman and Hugh Woodin, World Scientific Publishing, 2015, 39-121.
It appears as Corollary 5.2.8 which is a special case of a general statement (Theorem 5.6).