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Russian Mathematical Surveys, 2010, Volume 65, Issue 5, Pages 857–899
DOI: https://doi.org/10.1070/RM2010v065n05ABEH004703 (Mi rm9378) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Gödel incompleteness theorems and the limits of their applicability. I

L. D. Beklemishev

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (721 kB) Citations (10) Russian version article
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DOI: https://doi.org/10.1070/RM2010v065n05ABEH004703
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.
Received: 20.08.2010
Bibliographic databases:
Document Type: Article
UDC: 510.2+510.6
MSC: Primary 03F40; Secondary 03F25, 03F30, 03F45
Language: English
Original paper language: Russian
Citation: L. D. Beklemishev, “Gödel incompleteness theorems and the limits of their applicability. I”, Russian Math. Surveys, 65:5 (2010), 857–899
Citation in format AMSBIB
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\jour Russian Math. Surveys
\yr 2010
\vol 65
\issue 5
\pages 857--899
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  • https://www.mathnet.ru/eng/rm/v65/i5/p61
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:2461
    Russian version PDF:1325
    English version PDF:35
    References:167
    First page:76
     
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