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Mathematics of the USSR-Izvestiya, 1971, Volume 5, Issue 1, Pages 1–28
DOI: https://doi.org/10.1070/IM1971v005n01ABEH001004 (Mi im1910) 		 
This article is cited in 23 scientific papers (total in 24 papers)

Diophantine representation of enumerable predicates

Yu. V. Matiyasevich
English version PDF (1006 kB) Citations (24)
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DOI: https://doi.org/10.1070/IM1971v005n01ABEH001004
Abstract: An example is given of a diophantine relation which has exponential growth. This, together with the well-known results of Martin Davis, Hilary Putnam, and Julia Robinson, yields a proof that every enumerable predicate is Diophantine. This theorem implies that Hilbert's tenth problem is algorithmically unsolvable.
Received: 17.09.1970
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1971, Volume 35, Issue 1, Pages 3–30
Bibliographic databases:
UDC: 511
MSC: 02E10, 10B99, 10N05
Language: English
Original paper language: Russian
Citation: Yu. V. Matiyasevich, “Diophantine representation of enumerable predicates”, Izv. Akad. Nauk SSSR Ser. Mat., 35:1 (1971), 3–30; Math. USSR-Izv., 5:1 (1971), 1–28
Citation in format AMSBIB
\Bibitem{Mat71}
\by Yu.~V.~Matiyasevich
\paper Diophantine representation of enumerable predicates
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 1
\pages 3--30
\mathnet{http://mi.mathnet.ru/im1910}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1990738}
\zmath{https://zbmath.org/?q=an:0219.02035}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 1
\pages 1--28
\crossref{https://doi.org/10.1070/IM1971v005n01ABEH001004}
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:870
    Russian version PDF:449
    English version PDF:32
    References:68
    First page:3
     
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