# Sh:1082

• Kaplan, I., & Shelah, S. (2017). Decidability and classification of the theory of integers with primes. J. Symb. Log., 82(3), 1041–1050.
• Abstract:
We show that under Dickson’s conjecture about the distribution of primes in the natural numbers, the theory Th\left(\mathbb{Z},+,1,0, Pr\right) where Pr is a predicate for the prime numbers and their negations is decidable, unstable and supersimple. This is in contrast with Th\left(\mathbb{Z},+,0,Pr,<\right) which is known to be undecidable by the works of Jockusch, Bateman and Woods.
• published version (10p)
Bib entry
@article{Sh:1082,
author = {Kaplan, Itay and Shelah, Saharon},
title = {{Decidability and classification of the theory of integers with primes}},
journal = {J. Symb. Log.},
fjournal = {The Journal of Symbolic Logic},
volume = {82},
number = {3},
year = {2017},
pages = {1041--1050},
issn = {0022-4812},
mrnumber = {3694340},
mrreviewer = {Shih Ping Tung},
mrclass = {03C45 (03B25 03F30 11A41)},
doi = {10.1017/jsl.2017.16},
note = {\href{https://arxiv.org/abs/1601.07099}{arXiv: 1601.07099}},
arxiv_number = {1601.07099}
}