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Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number

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Abstract

It is known that the arithmetic of natural and integer numbers is unsolvable. Even the universal theory of integers with addition and multiplication is unsolvable. It is proved herein that an elementary theory of integers with addition, order, and multiplication by one arbitrary number is solvable and multiplication by the power of one number is unsolvable. For a certain n, the universal theory of integers with addition and n multiplications by an arbitrary number is also unsolvable.

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Literature cited

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Authors and Affiliations

  1. Irkut-sk State University, USSR

    Yu. G. Penzin

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  1. Yu. G. Penzin
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Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 667–675, May, 1973.

In conclusion, I am grateful to A. I. Kokorin for assistance in selecting topic.

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Penzin, Y.G. Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number. Mathematical Notes of the Academy of Sciences of the USSR 13, 401–405 (1973). https://doi.org/10.1007/BF01147467

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  • DOI: https://doi.org/10.1007/BF01147467

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