, Volume 33, Issue 4, pp 265-281

The prime number theorem and fragments ofP A

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We show that versions of the prime number theorem as well as equivalent statements hold in an arbitrary model of 0+exp.

A part of the preparation of this paper was done while the authors were visiting the University of Oxford in the spring of 1992; their visit was partially supported by the University of Crete (grant no. 185) and the British Council. The authors thank Drs. R. Kaye and A. Wilkie for useful discussions and the Mathematical Institute of the University of Oxford for their hospitality; they also thank Dr. K. Skandalis for pointing out an error in an earlier proof of Theorem 3.3 and the two referees, for suggesting Lemma 1.13 as a common generalization of some earlier Lemmas and for many other comments, which helped to improve this paper