# Sh:1082

- Kaplan, I., & Shelah, S. (2017).
*Decidability and classification of the theory of integers with primes*. J. Symb. Log.,**82**(3), 1041–1050. arXiv: 1601.07099 DOI: 10.1017/jsl.2017.16 MR: 3694340 -
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}, 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} }