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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 882–887
DOI: https://doi.org/10.17377/semi.2016.13.070
(Mi semr720)
 

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

Mathematical logic, algebra and number theory

Generic undecidability of existential theory of integer numbers ring

A. N. Rybalov

Sobolev Institute of Mathematics, Pevtsova str. 13, Omsk 644043, Russia
Full-text PDF (131 kB) Citations (2)
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Abstract: Famous theorem of Matiyasevich about undecidability of Hilbert’s thenth problem implies that existential theory of ring of integer numbers is undecidable. In this paper we prove that this theory remains undecidable if we restrict the set of all existential arithmetic statements by any recursive subsets of almost all statements (so called generic sets).
Keywords: existential theory of ring of integer numbers, generic complexity.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00068_а
Received March 24, 2016, published October 20, 2016
Bibliographic databases:
Document Type: Article
UDC: 510.652
MSC: 11U99
Language: Russian
Citation: A. N. Rybalov, “Generic undecidability of existential theory of integer numbers ring”, Sib. Èlektron. Mat. Izv., 13 (2016), 882–887
Citation in format AMSBIB
\Bibitem{Ryb16}
\by A.~N.~Rybalov
\paper Generic undecidability of existential theory of integer numbers ring
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 882--887
\mathnet{http://mi.mathnet.ru/semr720}
\crossref{https://doi.org/10.17377/semi.2016.13.070}
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  • https://www.mathnet.ru/eng/semr/v13/p882
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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