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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 5(395), Pages 61–106 (Mi umn9378)  

This article is cited in 2 scientific papers (total in 2 papers)

Gödel incompleteness theorems and the limits of their applicability. I

L. D. Beklemishev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This is a survey of results related to the Gödel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Gödel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed.
Bibliography: 68 titles.

Keywords: Gödel theorems, incompleteness, proof, computability.

DOI: https://doi.org/10.4213/rm9378

Full text: PDF file (932 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2010, 65:5, 857–899

Bibliographic databases:

Document Type: Article
UDC: 510.2+510.6
MSC: Primary 03F40; Secondary 03F25, 03F30, 03F45
Received: 20.08.2010

Citation: L. D. Beklemishev, “Gödel incompleteness theorems and the limits of their applicability. I”, Uspekhi Mat. Nauk, 65:5(395) (2010), 61–106; Russian Math. Surveys, 65:5 (2010), 857–899

Citation in format AMSBIB
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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. A. V. Bessonov, “O dvukh nevernykh dogmakh, svyazannykh so vtoroi teoremoi Gedelya o nepolnote arifmetiki. I”, Filosofiya nauki, 2014, no. 4(63), 12–31  mathscinet  elib
    2. Salehi S., Seraji P., “On Constructivity and the Rosser Property: a Closer Look At Some Gödelean Proofs”, Ann. Pure Appl. Log., 169:10 (2018), 971–980  crossref  mathscinet  zmath  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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