Decidability and classification of the theory of integers with primes
Logic
2016-02-16 v2
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.
Keywords
Cite
@article{arxiv.1601.07099,
title = {Decidability and classification of the theory of integers with primes},
author = {Itay Kaplan and Saharon Shelah},
journal= {arXiv preprint arXiv:1601.07099},
year = {2016}
}