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On ordering and multiplication of natural numbers

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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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Authors and Affiliations

  1. Philosophical Faculty of the Charles University, Celetna 20, 11642 Praha 1, Czech Republic (e-mail: Kamila.Bendova@ff.cuni.cz) , , , , , , CZ

    Kamila Bendová

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  1. Kamila Bendová
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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

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