The theory of integer multiplication with order restricted to primes is decidable

Publisher: Cambridge University Press

E-ISSN: 1943-5886|62|1|123-130

ISSN: 0022-4812

Source: The Journal of Symbolic Logic, Vol.62, Iss.1, 1997-03, pp. : 123-130

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Abstract

We show here that the first order theory of the positive integers equipped with multiplication remains decidable when one adds to the language the usual order restricted to the prime numbers. We see moreover that the complexity of the latter theory is a tower of exponentials, of height O(n).