As the title stated, I'm an amateur in the number theory that has just approached hilbert's tenth problem and the demonstration given by Matijasevic, but I couldn't find much on it, and what I could find was overly complicated for my self taught knowledge or just poorly traslated from russian up to the point of becoming impossible to read. Can someone please give me an explanation of the demonstration without taking for granted my knowledge of PhD mathematics?
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1$\begingroup$ This is a very accessible book. It explains the details and provides motivation. $\endgroup$– Andrés E. CaicedoCommented Sep 11, 2020 at 23:33
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$\begingroup$ There is also this book. $\endgroup$– Andrés E. CaicedoCommented Sep 11, 2020 at 23:34
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$\begingroup$ @AndrésE.Caicedo I was looking for something more synthetic, or is the explanation just to big to fit somewhere else than in a book? $\endgroup$– thatguythatroamsforumsCommented Sep 11, 2020 at 23:40
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1$\begingroup$ For instance, one can state the result as saying that (PA proves that) $\Sigma^0_1=\Sigma_1$. I don't know whether this makes sense to you or, even if it does, whether you see why it is indeed a solution to the tenth problem. $\endgroup$– Andrés E. CaicedoCommented Sep 12, 2020 at 0:35
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1$\begingroup$ My suggestion is that you state in the body of the problem what your background is. For instance, are you familiar with Turing machines? With first-order logic? In terms of number-theoretic prerequisites, not much is needed. Some familiarity with Pell equations is probably enough. $\endgroup$– Andrés E. CaicedoCommented Sep 12, 2020 at 0:37
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