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arXiv:1601.07099 [math.LO]AbstractReferencesReviewsResources

Decidability and classification of the theory of integers with primes

Itay Kaplan, Saharon Shelah

Published 2016-01-26Version 1

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.

Categories: math.LO
Subjects: 03C45, 03F30, 03B25, 11A41
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