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Uspekhi Mat. Nauk, 1974, Volume 29, Issue 1(175), Pages 3–47 (Mi umn4322)  

This article is cited in 3 scientific papers (total in 3 papers)

An elementary exposition of Gödel's incompleteness theorem

V. A. Uspenskii


Abstract: Godel's incompleteness theorem states that there is no system of axioms and rules of inference such that the totality of all assertions deducible from the axioms is the same as the totality of all true assertions in arithmetic (indeed, for every consistent system one can construct effectively a true but unprovable assertion). The present article is devoted to a proof of this theorem, based on the concepts and methods of the theory of algorithms; the necessary information from the theory of algorithms is provided. The paper does not require specialized knowledge of any kind (in particular, none from mathematical logic), but assumes only a familiarity with elementary mathematical terminology and symbolism.

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English version:
Russian Mathematical Surveys, 1974, 29:1, 63–106

Bibliographic databases:

UDC: 517.19
MSC: 03F40, 03F50, 03E65, 03B65
Received: 08.10.1973

Citation: V. A. Uspenskii, “An elementary exposition of Gödel's incompleteness theorem”, Uspekhi Mat. Nauk, 29:1(175) (1974), 3–47; Russian Math. Surveys, 29:1 (1974), 63–106

Citation in format AMSBIB
\Bibitem{Usp74}
\by V.~A.~Uspenskii
\paper An elementary exposition of G\"odel's incompleteness theorem
\jour Uspekhi Mat. Nauk
\yr 1974
\vol 29
\issue 1(175)
\pages 3--47
\mathnet{http://mi.mathnet.ru/umn4322}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=398761}
\zmath{https://zbmath.org/?q=an:0291.02001|0299.02002}
\transl
\jour Russian Math. Surveys
\yr 1974
\vol 29
\issue 1
\pages 63--106
\crossref{https://doi.org/10.1070/RM1974v029n01ABEH001280}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. G. Grigoryan, “On convergence of Fourier series in complete orthonormal systems in the $L^1$-metric and almost everywhere”, Math. USSR-Sb., 70:2 (1991), 445–466  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. L. D. Beklemishev, “Gödel incompleteness theorems and the limits of their applicability. I”, Russian Math. Surveys, 65:5 (2010), 857–899  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Saifullaev Sh.R., “O vvedenii energodeneg v ekonomiku”, Ekonomika i predprinimatelstvo, 7:1 (2013), 359–365  elib
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