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Matematicheskie Zametki, 1973, Volume 13, Issue 5, Pages 667–675 (Mi mzm7170)  
This article is cited in 4 scientific papers (total in 4 papers)

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

Yu. G. Penzin

Irkutsk State University
Full-text PDF (662 kB) Citations (4)
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.
Received: 31.03.1971
English version:
Mathematical Notes, 1973, Volume 13, Issue 5, Pages 401–405
DOI: https://doi.org/10.1007/BF01147467
Bibliographic databases:
UDC: 517.11
Language: Russian
Citation: Yu. G. Penzin, “Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number”, Mat. Zametki, 13:5 (1973), 667–675; Math. Notes, 13:5 (1973), 401–405
Citation in format AMSBIB
\Bibitem{Pen73}
\by Yu.~G.~Penzin
\paper Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number
\jour Mat. Zametki
\yr 1973
\vol 13
\issue 5
\pages 667--675
\mathnet{http://mi.mathnet.ru/mzm7170}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=323551}
\zmath{https://zbmath.org/?q=an:0274.02019|0267.02035}
\transl
\jour Math. Notes
\yr 1973
\vol 13
\issue 5
\pages 401--405
\crossref{https://doi.org/10.1007/BF01147467}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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