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Zapiski Nauchnykh Seminarov LOMI, 1972, Volume 32, Pages 77–84 (Mi znsl2567)  

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

Arithmetical representations of recursively enumerable sets with a small number of quantifiers

Yu. V. Matiyasevich
Full-text PDF (340 kB) Citations (2)
Abstract: It is shown that every recursively enumerable set $M$ of positive integers can be represented in each of the following forms:
\begin{align} a\in M&\Leftrightarrow\exists_p\exists_s\&_{i=1}^\pi\exists_v[A_i(a,p,s,v)>0],\notag\\ a\in M&\Leftrightarrow\exists_s\&_{i=1}^\pi\exists_p\exists_v[B_i(a,p,s,v)>0],\notag\\ a\in M&\Leftrightarrow\exists_t\forall y_{\leq t} \exists_v\exists_w[C(a,t,y,v,w)=0].\notag \end{align}
Here $\pi$ is a particular integer, $A_i$, $B_i$, $C$ are polynomials with integer coefficients, $a$, $p$, $s$, $t$, $v$, $w$, $y$ ware variables for positive integers.
Bibliographic databases:
Language: Russian
Citation: Yu. V. Matiyasevich, “Arithmetical representations of recursively enumerable sets with a small number of quantifiers”, Studies in constructive mathematics and mathematical logic. Part V, Zap. Nauchn. Sem. LOMI, 32, "Nauka", Leningrad. Otdel., Leningrad, 1972, 77–84
Citation in format AMSBIB
\Bibitem{Mat72}
\by Yu.~V.~Matiyasevich
\paper Arithmetical representations of recursively enumerable sets with a~small number of quantifiers
\inbook Studies in constructive mathematics and mathematical logic. Part~V
\serial Zap. Nauchn. Sem. LOMI
\yr 1972
\vol 32
\pages 77--84
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2567}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=344095}
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  • https://www.mathnet.ru/eng/znsl/v32/p77
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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