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arXiv · 1601.07099

Decidability and classification of the theory of integers with primes

Itay Kaplan·Saharon Shelah
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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.

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Itay Kaplan, Saharon Shelah. 2016-02-14. Decidability and classification of the theory of integers with primes. https://arxiv.org/abs/1601.07099

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