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Algebra i logika, 2002, Volume 41, Number 2, Pages 143–154 (Mi al177)  

This article is cited in 31 scientific papers (total in 31 papers)

Friedberg Numberings of Families of $n$-Computably Enumerable Sets

S. S. Goncharova, S. Lemppb, R. Solomonb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b University of Wisconsin-Madison
References:
Abstract: We establish a number of results on numberings, in particular, on Friedberg numberings, of families of d.c.e. sets. First, it is proved that there exists a Friedberg numbering of the family of all d.c.e. sets. We also show that this result, patterned on Friedberg's famous theorem for the family of all c.e. sets, holds for the family of all $n$-c.e. sets for any $n>2$. Second, it is stated that there exists an infinite family of d. c. e. sets without a Friedberg numbering. Third, it is shown that there exists an infinite family of c. e. sets (treated as a family of d. c. e. sets) with a numbering which is unique up to equivalence. Fourth, it is proved that there exists a family of d. c. e. sets with a least numbering (under reducibility) which is Friedberg but is not the only numbering (modulo reducibility).
Received: 22.11.2000
English version:
Algebra and Logic, 2002, Volume 41, Issue 2, Pages 81–86
DOI: https://doi.org/10.1023/A:1015352513117
Bibliographic databases:
UDC: 510.10+510.57
Language: Russian
Citation: S. S. Goncharov, S. Lempp, R. Solomon, “Friedberg Numberings of Families of $n$-Computably Enumerable Sets”, Algebra Logika, 41:2 (2002), 143–154; Algebra and Logic, 41:2 (2002), 81–86
Citation in format AMSBIB
\Bibitem{GonLemSol02}
\by S.~S.~Goncharov, S.~Lempp, R.~Solomon
\paper Friedberg Numberings of Families of $n$-Computably Enumerable Sets
\jour Algebra Logika
\yr 2002
\vol 41
\issue 2
\pages 143--154
\mathnet{http://mi.mathnet.ru/al177}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1922986}
\zmath{https://zbmath.org/?q=an:1063.03028}
\transl
\jour Algebra and Logic
\yr 2002
\vol 41
\issue 2
\pages 81--86
\crossref{https://doi.org/10.1023/A:1015352513117}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846184874}
Linking options:
  • https://www.mathnet.ru/eng/al177
  • https://www.mathnet.ru/eng/al/v41/i2/p143
  • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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    Full-text PDF :159
    References:55
    First page:1
     
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