Submission date: 26 January 2016

Abstract:

We show that under Dickson's conjecture about the distribution of primes in the natural numbers, the theory Th(Z,+,1,0,Pr) where Pr is a predicate for the prime numbers and their negations is decidable, unstable and supersimple. This is in contrast with Th(Z,+,0,Pr,<) which is known to be undecidable by the works of Jockusch, Bateman and Woods.

Mathematics Subject Classification: 03C45, 03F30, 03B25, 11A41

Keywords and phrases:

Full text arXiv 1601.07099: pdf, ps.