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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 128–143 (Mi tm3346)  
This article is cited in 3 scientific papers (total in 3 papers)

What can and cannot be done with Diophantine problems

Yu. V. Matiyasevich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (245 kB) Citations (3)
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Abstract: This survey presents various theorems (obtained mainly by specialists in mathematical logic and computability theory) stating the impossibility of algorithms for solving certain Diophantine problems. Often the technique developed for obtaining such “negative” results also allows one to prove many “positive” theorems on the possibility of formulating Diophantine problems with special properties. This survey also lists a number of questions that remain open.
Received in February 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 118–132
DOI: https://doi.org/10.1134/S0081543811080074
Bibliographic databases:
Document Type: Article
UDC: 510.6+511
Language: Russian
Citation: Yu. V. Matiyasevich, “What can and cannot be done with Diophantine problems”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 128–143; Proc. Steklov Inst. Math., 275 (2011), 118–132
Citation in format AMSBIB
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\pages 128--143
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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