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Preprint Number 993

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993. Itay Kaplan and Saharon Shelah
Decidability and classification of the theory of integers with primes

Submission date: 26 January 2016


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

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Full text arXiv 1601.07099: pdf, ps.

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