Decidability and classification of the theory of integers with primes
classification
🧮 math.LO
keywords
numbersprimestheorybatemanclassificationconjecturecontrastdecidability
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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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