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

This article is cited in 18 scientific papers (total in 18 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

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).

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English version:
Algebra and Logic, 2002, 41:2, 81–86

Bibliographic databases:

UDC: 510.10+510.57
Received: 22.11.2000

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
\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
\jour Algebra and Logic
\yr 2002
\vol 41
\issue 2
\pages 81--86

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    This publication is cited in the following articles:
    1. Badaev S.A., Talasbaeva Zh.T., “Computable numberings in the hierarchy of Ershov”, Mathematical Logic in Asia, 2006, 17–30  crossref  mathscinet  zmath  adsnasa  isi
    2. Brodhead P., Cenzer D., “Effectively closed sets and enumerations”, Archive For Mathematical Logic, 46:7–8 (2008), 565–582  crossref  mathscinet  zmath  isi  scopus
    3. S. S. Goncharov, N. T. Kogabaev, “O $\Sigma^0_1$-klassifikatsii otnoshenii na vychislimykh strukturakh”, Vestn. NGU. Ser. matem., mekh., inform., 8:4 (2008), 23–32  mathnet
    4. S. S. Ospichev, “Some Properties of Numberings in Various Levels in Ershov's Hierarchy”, J. Math. Sci., 188:4 (2013), 441–448  mathnet  crossref
    5. S. S. Ospichev, “Infinite family of $\Sigma_a^{-1}$-Sets with only One Computable Numbering”, J. Math. Sci., 188:4 (2013), 449–451  mathnet  crossref
    6. N. A. Bazhenov, “The branching theorem and computable categoricity in the Ershov hierarchy”, Algebra and Logic, 54:2 (2015), 91–104  mathnet  crossref  crossref  mathscinet  isi
    7. S. S. Ospichev, “Computable families of sets in Ershov hierarchy without principal numberings”, J. Math. Sci., 215:4 (2016), 529–536  mathnet  crossref
    8. S. S. Ospichev, “Friedberg numberings in the Ershov hierarchy”, Algebra and Logic, 54:4 (2015), 283–295  mathnet  crossref  crossref  mathscinet  isi
    9. Badaev S.A., Manat M., Sorbi A., “Friedberg Numberings in the Ershov Hierarchy”, Arch. Math. Log., 54:1-2 (2015), 59–73  crossref  mathscinet  zmath  isi  elib  scopus
    10. Lange K. Miller R. Steiner R.M., “Classifications of Computable Structures”, Notre Dame J. Form. Log., 59:1 (2018), 35–59  crossref  mathscinet  zmath  isi  scopus
    11. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Positive presentations of families relative to $e$-oracles”, Siberian Math. J., 59:4 (2018), 648–656  mathnet  crossref  crossref  isi  elib
    12. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov, “Positive presentations of families in relation to reducibility with respect to enumerability”, Algebra and Logic, 57:4 (2018), 320–323  mathnet  crossref  crossref  isi
    13. M. V. Dorzhieva, “Odnoznachnaya numeratsiya dlya semeistva vsekh $\Sigma^{1}_{2}$-mnozhestv”, Sib. zhurn. chist. i prikl. matem., 18:2 (2018), 47–52  mathnet  crossref
    14. S. S. Ospichev, “Fridbergovy numeratsii semeistv chastichno vychislimykh funktsionalov”, Sib. elektron. matem. izv., 16 (2019), 331–339  mathnet  crossref
    15. N. A. Bazhenov, B. S. Kalmurzaev, “Rogers semilattices for families of equivalence relations in the Ershov hierarchy”, Siberian Math. J., 60:2 (2019), 223–234  mathnet  crossref  crossref  isi  elib
    16. M. V. Dorzhieva, “Vychislimye numeratsii semeistv beskonechnykh mnozhestv”, Algebra i logika, 58:3 (2019), 334–343  mathnet  crossref
    17. S. Boyadzhiiska, K. Lange, E. Raz, R. Skenlon, Dzh. Vollbaum, Kh. Chzhan, “Klassifikatsii opredelimykh podmnozhestv”, Algebra i logika, 58:5 (2019), 574–608  mathnet  crossref
    18. Herbert I. Jain S. Lempp S. Mustafa M. Stephan F., “Reductions Between Types of Numberings”, Ann. Pure Appl. Log., 170:12 (2019), UNSP 102716  crossref  mathscinet  isi  scopus
  • Алгебра и логика Algebra and Logic
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