Skip to main content
Log in

Linear Orderings of Low Degree

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We consider the class of so-called k-quasidiscrete linear orderings, show that every k-quasi-discrete ordering of low degree has a computable representation, and study estimates for the complexity of all isomorphisms constructed in the article.

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. Jockusch C. G. and Soare R. I., “Degrees of orderings not isomorphic to recursive linear orderings,” Ann. Pure Appl. Logic, 52, 39–61 (1991).

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  3. Downey R. G. and Moses M. F., “On choice sets and strongly nontrivial self-embeddings of recursive linear orderings,” Z. Math. Logik Grundlag. Math., 35, 237–246 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  4. Downey R. G., “Computability theory and linear orderings,” in: ed]Ershov_Yu. L., Goncharov S. S., Nerode A., Remmel J. B. (eds.), Handbook of Recursive Mathematics, Elsevier, Amsterdam, 1998. Ch. 14 (Stud. Logic Found. Math.; V. 139).

    Google Scholar 

  5. Frolov A. S., “▵0 2-Copies of linear orderings,” Algebra and Logic, 45, No. 3, 201–209 (2006).

    Article  MathSciNet  Google Scholar 

  6. Soare R. I., Recursively Enumerable Sets and Degrees, Springer-Verlag, Heidelberg (1987).

    Google Scholar 

  7. Rosenstein J. G., Linear Orderings, Academic Press, New York (1982).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. N. Frolov.

Additional information

Original Russian Text Copyright Sc 2010 Frolov A. N.

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 5, pp. 1147–1162, September–October, 2010

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frolov, A.N. Linear Orderings of Low Degree. Sib Math J 51, 913–925 (2010). https://doi.org/10.1007/s11202-010-0091-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-010-0091-7

Keywords

Navigation