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Mathematics of the USSR-Sbornik, 1976, Volume 30, Issue 3, Pages 321–340
DOI: https://doi.org/10.1070/SM1976v030n03ABEH002277 (Mi sm2904) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On some properties of the Medvedev lattice

E. Z. Dyment
English version PDF (1466 kB) Citations (11)
References:
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DOI: https://doi.org/10.1070/SM1976v030n03ABEH002277
Abstract: This article investigates the structure of the lattice of degrees of difficulty, introduced by Medvedev. In particular, an answer is given to Rogers' question: Is being a degree of solvability a lattice-theoretic property? It is proved that for every degree except the smallest, the smallest nonrecursive, and the largest degrees, there exists a degree not comparable with it. Also analyzed are conditions under which there are no degrees lying strictly between two given degrees. The final consideration is a topological approach to certain questions about the structure of the Medvedev lattice.
Bibliography: 2 titles.
Received: 21.04.1975
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1976, Volume 101(143), Number 3(11), Pages 360–379
Bibliographic databases:
UDC: 517.11+518.6
MSC: Primary 02F29, 02F30, 02F40, 06A20; Secondary 02F20, 02F25, 54C50
Language: English
Original paper language: Russian
Citation: E. Z. Dyment, “On some properties of the Medvedev lattice”, Math. USSR-Sb., 30:3 (1976), 321–340
Citation in format AMSBIB
\Bibitem{Dym76}
\by E.~Z.~Dyment
\paper On some properties of the Medvedev lattice
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 3
\pages 321--340
\mathnet{http://mi.mathnet.ru//eng/sm2904}
\crossref{https://doi.org/10.1070/SM1976v030n03ABEH002277}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=432433}
\zmath{https://zbmath.org/?q=an:0353.02019}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1976FN58700004}
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  • https://doi.org/10.1070/SM1976v030n03ABEH002277
  • https://www.mathnet.ru/eng/sm/v143/i3/p360
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:272
    Russian version PDF:100
    English version PDF:15
    References:56
     
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