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DECIDABILITY AND CLASSIFICATION OF THE THEORY OF INTEGERS WITH PRIMES
Published online by Cambridge University Press: 08 September 2017
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.
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- Copyright © The Association for Symbolic Logic 2017
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