116b- Lecture 18

Hilbert’s tenth problem asks whether there is an algorithm that given a polynomial with integer coefficients (in an arbitrary number of variables) determines whether it has integer roots. A celebrated theorem of Davis, Matiyasevich, Putnam and Robinson shows that this is not the case. Their result shows that the class of Diophantine sets coincides with the a priori larger class of r.e. (or \Sigma_1)  sets.

We proved this result under the assumption that exponentiation is Diophantine. This is the key result, and will be dealt with in the following lecture.


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