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Zapiski Nauchnykh Seminarov LOMI, 1976, Volume 60, Pages 15–28 (Mi znsl2066)  
This article is cited in 6 scientific papers (total in 6 papers)

Decidability of the universal theory of natural numbers with addition and divisibility

A. P. Beltiukov
Full-text PDF (620 kB) Citations (6)
Abstract: The class of all quantifier-free formulas constructed from atomic formulas of the form $(x+y=z)$, $(x=1)$, and $(x/y)$ is considered, where the predicate symbol “|” is interpreted as the divisibility relation on nonnegative integers. The decidability isproved of the set of all formulas of this form which are true for at least one choice of values for the variables. This result is equivalent to the decidability of the universal theory of natural numbers with addition and divisibility.
English version:
Journal of Soviet Mathematics, 1980, Volume 14, Issue 5, Pages 1436–1444
DOI: https://doi.org/10.1007/BF01693974
Bibliographic databases:
UDC: 51.01:164
Language: Russian
Citation: A. P. Beltiukov, “Decidability of the universal theory of natural numbers with addition and divisibility”, Studies in constructive mathematics and mathematical logic. Part VII, Zap. Nauchn. Sem. LOMI, 60, "Nauka", Leningrad. Otdel., Leningrad, 1976, 15–28; J. Soviet Math., 14:5 (1980), 1436–1444
Citation in format AMSBIB
\Bibitem{Bel76}
\by A.~P.~Beltiukov
\paper Decidability of the universal theory of natural numbers with addition and divisibility
\inbook Studies in constructive mathematics and mathematical logic. Part~VII
\serial Zap. Nauchn. Sem. LOMI
\yr 1976
\vol 60
\pages 15--28
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2066}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=538174}
\zmath{https://zbmath.org/?q=an:0449.03011|0345.02035}
\transl
\jour J. Soviet Math.
\yr 1980
\vol 14
\issue 5
\pages 1436--1444
\crossref{https://doi.org/10.1007/BF01693974}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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