Skip to main content
Log in

Δ 02 -copies of linear orderings

  • Published:
Algebra and Logic Aims and scope


It is proved that, for any n ∈ ω, there exist countable linear orderings Ln whose Δ 02 -spectrum consists of exactly all non n-low Δ 02 -degrees. Properties of such orderings are examined, for n = 1 and n = 2.

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


  1. R. I. Soare, Recursively Enumerable Sets and Degrees, Springer, Berlin (1987).

    Google Scholar 

  2. T. Slaman, “Relative to any nonrecursive,” Proc. Am. Math. Soc., 126, No. 7, 2117–2122 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Wehner, “Enumeration, countable structure and Turing degrees,” Proc. Am. Math. Soc., 126, No. 7, 2131–2139 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  4. R. G. Downey, “On presentations of algebraic structures,” in Complexity, Logic, and Recursion Theory, Lect. Notes Pure Appl. Math., Vol. 187, Marcel Dekker, New York (1997), pp. 157–205.

    Google Scholar 

  5. R. Miller, “The Δ 02 spectrum of a linear ordering,” J. Symb. Log., 66, No. 2, 470–486 (2001).

    MATH  Google Scholar 

  6. S. S. Goncharov, V. S. Harizanov, J. F. Knight, C. McCoy, R. Miller, and R. Solomon, Enumerations in Computable Structure Theory, in press.

  7. R. G. Downey and J. F. Knight, “Orderings with α-th jump degree 0(α),” Proc. Am. Math. Soc., 114, No. 2, 545–552 (1992).

    Article  MathSciNet  Google Scholar 

  8. R. Watnick, “A generalization of Tennenbaum’s theorem on effectively finite recursive linear orderings,” J. Symb. Log., 49, 563–569 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  9. D. K. Roy and R. Watnik, “Finite condensations of recursive linear orderings,” Stud. Log., 47, No. 4, 311–317 (1988).

    Article  Google Scholar 

  10. C. J. Ash, C. Jockusch, and J. F. Knight, “Jumps of orderings,” Trans. Am. Math. Soc., 319, No. 2, 573–599 (1990).

    Article  MathSciNet  Google Scholar 

  11. R. G. Downey and M. F. Moses, “On choice sets and strongly nontrivial self-embeddings of recursive linear orderings,” Z. Math. Logik Grund. Math., 35, No. 3, 237–246 (1989).

    MathSciNet  Google Scholar 

  12. R. G. Downey and C. G. Jockusch, “Every low Boolean algebra is isomorphic to a recursive one,” Proc. Am. Math. Soc., 122, No. 3, 871–880 (1994).

    Article  MathSciNet  Google Scholar 

  13. P. E. Alaev and A. N. Frolov, “Computability on linear orderings expanded by predicates,” in press.

Download references

Author information

Authors and Affiliations


Additional information

Supported by RFBR grant No. 02-01-00169 and by RF Ministry of Education grant No. E02-1.0-177.


Translated from Algebra i Logika, Vol. 45, No. 3, pp. 354–370, May–June, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frolov, A.N. Δ 02 -copies of linear orderings. Algebr Logic 45, 201–209 (2006).

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: