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Dokl. Akad. Nauk SSSR, 1970, Volume 191, Number 2, Pages 279–282 (Mi dan35274)  

This article is cited in 26 scientific papers (total in 26 papers)

MATHEMATICS

The Diophantineness of enumerable sets

Yu. V. Matiyasevich

Leningrad Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences

Full text: PDF file (525 kB)

Bibliographic databases:
UDC: 51.01:518.5+511.5
Presented: И. М. Виноградов
Received: 05.02.1970

Citation: Yu. V. Matiyasevich, “The Diophantineness of enumerable sets”, Dokl. Akad. Nauk SSSR, 191:2 (1970), 279–282

Citation in format AMSBIB
\Bibitem{Mat70}
\by Yu.~V.~Matiyasevich
\paper The Diophantineness of enumerable sets
\jour Dokl. Akad. Nauk SSSR
\yr 1970
\vol 191
\issue 2
\pages 279--282
\mathnet{http://mi.mathnet.ru/dan35274}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0258744}
\zmath{https://zbmath.org/?q=an:0212.33401}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. V. Matiyasevich, “Diophantine representation of enumerable predicates”, Math. USSR-Izv., 5:1 (1971), 1–28  mathnet  crossref  mathscinet  zmath
    2. Yu. V. Matiyasevich, “Diophantine sets”, Russian Math. Surveys, 27:5 (1972), 124–164  mathnet  crossref  mathscinet  zmath
    3. L. A. Bokut', “Unsolvability of the equality problem and subalgebras of finitely presented Lie algebras”, Math. USSR-Izv., 6:6 (1972), 1153–1199  mathnet  crossref  mathscinet  zmath
    4. A. I. Kokorin, A. G. Pinus, “Decidability problems of extended theories”, Russian Math. Surveys, 33:2 (1978), 53–96  mathnet  crossref  mathscinet  zmath
    5. J. Math. Sci. (N. Y.), 130:2 (2005), 4607–4619  mathnet  crossref  mathscinet  zmath
    6. Yu. V. Matiyasevich, “A Diophantine Representation of Bernoulli Numbers and Its Applications”, Proc. Steklov Inst. Math., 242 (2003), 86–91  mathnet  mathscinet  zmath
    7. E. V. Kuzmin, D. Yu. Chalyi, “O yazykakh avtomatnykh schetchikovykh mashin”, Model. i analiz inform. sistem, 17:2 (2010), 48–71  mathnet
    8. J. Math. Sci. (N. Y.), 171:6 (2010), 745–752  mathnet  crossref
    9. J. Math. Sci. (N. Y.), 171:6 (2010), 765–781  mathnet  crossref
    10. 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
    11. A. G. Myasnikov, N. S. Romanovskii, “Universal theories for rigid soluble groups”, Algebra and Logic, 50:6 (2012), 539–552  mathnet  crossref  mathscinet  zmath  isi
    12. Proc. Steklov Inst. Math., 274 (2011), 116–123  mathnet  crossref  mathscinet  isi  elib
    13. Yu. V. Matiyasevich, “What can and cannot be done with Diophantine problems”, Proc. Steklov Inst. Math., 275 (2011), 118–132  mathnet  crossref  mathscinet  isi  elib  elib
    14. S. Yu. Erofeev, “Diofantovost diskretnogo logarifma”, PDM, 2011, prilozhenie № 4, 31–32  mathnet
    15. V. A. Romankov, “Diofantova kriptografiya na beskonechnykh gruppakh”, PDM, 2012, no. 2(16), 15–42  mathnet
    16. S. Yu. Erofeev, V. A. Romankov, “O postroenii vozmozhno odnostoronnikh funktsii na osnove algoritmicheskoi nerazreshimosti problemy endomorfnoi svodimosti v gruppakh”, PDM, 2012, no. 3(17), 13–24  mathnet
    17. N. S. Romanovskii, “Universal theories for free solvable groups”, Algebra and Logic, 51:3 (2012), 259–263  mathnet  crossref  mathscinet  zmath  isi
    18. A. A. Knop, “Diophantine hierarchy”, J. Math. Sci. (N. Y.), 188:1 (2013), 59–69  mathnet  crossref  mathscinet
    19. J. Math. Sci. (N. Y.), 199:1 (2014), 36–52  mathnet  crossref  mathscinet
    20. E. I. Timoshenko, “Universal theory of a free polynilpotent group”, Izv. Math., 80:3 (2016), 623–632  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. A. N. Rybalov, “O genericheskoi slozhnosti problemy razreshimosti sistem diofantovykh uravnenii v forme Skolema”, PDM, 2017, no. 37, 100–106  mathnet  crossref
    22. A. S. Morozov, “On some reducibility and existential interpretability of structures”, Siberian Math. J., 58:2 (2017), 281–287  mathnet  crossref  crossref  isi  elib  elib
    23. A. Yu. Nikitin, A. N. Rybalov, “O slozhnosti problemy razreshimosti sistem uravnenii nad konechnymi chastichnymi poryadkami”, PDM, 2018, no. 39, 94–98  mathnet  crossref
    24. A. N. Rybalov, “O genericheskoi nerazreshimosti desyatoi problemy Gilberta dlya polinomialnykh derevev”, PDM, 2019, no. 44, 107–112  mathnet  crossref
    25. A. Yu. Nikitin, “Razreshimost ogranichennykh teorii klassa chastichnykh poryadkov”, PDM, 2019, no. 45, 6–12  mathnet  crossref
    26. B. Z. Moroz, A. A. Norkin, “On a Theorem of Matiyasevich”, Math. Notes, 108:3 (2020), 344–355  mathnet  crossref  crossref  isi
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