Abstract.
Even if the ordering of all natural number is (known to be) not definable from multiplication of natural numbers and ordering of primes, there is a simple axiom system in the language \((\times,<,1)\) such that the multiplicative structure of positive integers has a unique expansion by a linear order coinciding with the standard order for primes and satisfying the axioms – namely the standard one.
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Received: 3 December 1998
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Bendová, K. On ordering and multiplication of natural numbers. Arch Math Logic 40, 19–23 (2001). https://doi.org/10.1007/s001530050171
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DOI: https://doi.org/10.1007/s001530050171