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DECIDABILITY AND CLASSIFICATION OF THE THEORY OF INTEGERS WITH PRIMES

Published online by Cambridge University Press:  08 September 2017

ITAY KAPLAN  and
SAHARON SHELAH
ITAY KAPLAN
Affiliation:
THE HEBREW UNIVERSITY OF JERUSALEM EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS, GIVAT RAM JERUSALEM91904, ISRAELE-mail: [email protected]: https://sites.google.com/site/itay80/
SAHARON SHELAH
Affiliation:
THE HEBREW UNIVERSITY OF JERUSALEM EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS, GIVAT RAM JERUSALEM 91904, ISRAEL and DEPARTMENT OF MATHEMATICS HILL CENTER-BUSCH CAMPUS RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY 110 FRELINGHUYSEN ROAD PISCATAWAY, NJ08854-8019, USA E-mail: [email protected]: http://shelah.logic.at/
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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.

Keywords

03C4503F3003B2511A41model theorydecidabilityprimesDickson’s conjecture
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 3 , September 2017 , pp. 1041 - 1050
Copyright
Copyright © The Association for Symbolic Logic 2017 

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