RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zap. Nauchn. Sem. POMI: Year: Volume: Issue: Page: Find

 Zap. Nauchn. Sem. LOMI, 1976, Volume 60, Pages 15–28 (Mi znsl2066)

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

A. P. Beltiukov

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.

Full text: PDF file (620 kB)

English version:
Journal of Soviet Mathematics, 1980, 14:5, 1436–1444

Bibliographic databases:

UDC: 51.01:164

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://www.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} 

• http://mi.mathnet.ru/eng/znsl2066
• http://mi.mathnet.ru/eng/znsl/v60/p15

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. I. Kokorin, A. G. Pinus, “Decidability problems of extended theories”, Russian Math. Surveys, 33:2 (1978), 53–96