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

Published online by Cambridge University Press:  12 March 2014

Françoise Maurin
Françoise Maurin*
Affiliation:
G.R.A.L., Mathématiques, Université de Caen, 14 032 Caen Cedex, France
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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).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 123 - 130
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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