Skip to main content
Log in

Major Sets, Classes of Simple Sets, and \(Q \)-Complete Sets

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

Each nonrecursive recursively enumerable set is proved to have a \(Q\)-complete major subset. Classes of simple sets that contain \(Q\)-complete sets are determined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. E. Herrmann, “Classes of simple sets, filter properties, and their mutual position,” Seminarber. Humboldt-Univ. Berlin. Sekt. Math. (1984), no. 60, 60–72.

  2. R. Sh. Omanadze, “Classes of recursively enumerable sets and Q-reducibility,” Mat. Zametki [Math. Notes], 45 (1989), no. 2, 79–82.

    Google Scholar 

  3. H. Rogers, Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York-St Louis-San Francisco-Toronto-London-Sydney, 1967.

    Google Scholar 

  4. S. S. Marchenkov, “On a class of incomplete sets,” Mat. Zametki [Math. Notes], 20 (1976), no. 4, 473–478.

    Google Scholar 

  5. V. D. Solov′ev, “Q-reducibility and hyperhypersimple sets,” in: Probabilistic Methods and Cybernetics [in Russian], Kazan State Univ., Kazan, 1974, pp. 121–128.

    Google Scholar 

  6. J. T. Gill and P. H. Morris, “On subcreative sets and S-reducibility,” J. Symb. Logic, 39 (1974), no. 4, 669–677.

    Google Scholar 

  7. A. H. Lachlan, “On the lattice of recursively enumerable sets,” Trans. Amer. Math. Soc., 130 (1968), no. 1, 1–37.

    Google Scholar 

  8. E. Herrmann, “Die Verbandseigenschaften der rekursiv aufzählbaren Mengen,” Seminarber. Humboldt-Univ. Berlin. Sekt. Math. (1981), no. 36.

  9. M. Blum and I. Marques, “On complexity properties of recursively enumerable sets,” J. Symb. Logic, 38 (1973), no. 4, 579–593.

    Google Scholar 

  10. M. Lerman, “Some theorems of r-maximal sets and major subsets of recursively enumerable sets,” J. Symb. Logic, 36 (1971), 193–215.

    Google Scholar 

  11. A. N. Degtev, “On m-degrees of simple sets,” Algebra i Logika [Algebra and Logic], 11 (1972), no. 2, 130–139.

    Google Scholar 

  12. M. M. Arslanov, “On a class of hypersimple incomplete sets,” Mat. Zametki [Math. Notes], 38 (1985), no. 6, 872–874.

    Google Scholar 

  13. A. N. Degtev, “Certain classes of hyperimmune sets,” in: Algebraic Systems [in Russian], Irkutsk, 1976, pp. 21–36.

  14. R. W. Robinson, “Simplicity of recursively enumerable sets,” J. Symb. Logic, 32 (1967), no. 2, 162–172.

    Google Scholar 

  15. A. S. Morozov, “On a class of recursively enumerable sets,” Sibirsk. Mat. Zh. [Siberian Math. J.], 23 (1987), no. 2, 124–128.

    Google Scholar 

  16. A. N. Degtev, “Hereditory sets and truth-table reducibility,” Algebra i Logika [Algebra and Logic], 11 (1972), no. 3, 257–269.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Omanadze, R.S. Major Sets, Classes of Simple Sets, and \(Q \)-Complete Sets. Mathematical Notes 71, 90–97 (2002). https://doi.org/10.1023/A:1013930408357

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013930408357

Navigation