Characterization of prime numbers by Lukasiewicz's many-valued logics

Bulletin of the Section of Logic 13 (2):64-67 (1984)
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Abstract

In this note we construct finitely n-valued logic Kn such that it has tautologies iff n − 1 is a prime number. Moreover, we prove that Kn with respect to functional properties is Lukasiewicz’s n-valued logic Ln when n − 1 is a prime number. The proof in direct way shows the exceptional complexity of distributing prime numbers in natural series

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