DECIDABILITY AND CLASSIFICATION OF THE THEORY OF INTEGERS WITH PRIMES-Reference-Cited by-同舟云学术

DECIDABILITY AND CLASSIFICATION OF THE THEORY OF INTEGERS WITH PRIMES

Published:2017-09 Issue:3 Volume:82 Page:1041-1050
ISSN:0022-4812
Container-title:The Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

KAPLAN ITAY,SHELAH SAHARON

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

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