Submission date: 2 September 2013.

Abstract:

These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It also contains a sketch of the authors result that the integers are universally definable in the rationals.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1309.0441: pdf, ps.