Skip to main content
Log in

Cuts of Linear Orders

  • Published:
Order Aims and scope Submit manuscript

Abstract

We study the connection between the number of ascending and descending cuts of a linear order, its classical size, and its effective complexity (how much [how little] information can be encoded into it).

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. Alaev, P.E., Thurber, J., Frolov, A.N.: Computability on linear orderings enriched with predicates. Algebra Logic 48(5), 313–320 (2009)

    Article  MathSciNet  Google Scholar 

  2. Ash, C.J., Knight, J.: Computable structures and the hyperarithmetical hierarchy. In: Studies in Logic and the Foundations of Mathematics, vol. 144. North-Holland, Amsterdam (2000)

  3. Downey, R., Jockusch, C.G.: Every low Boolean algebra is isomorphic to a recursive one. Proc. Am. Math. Soc. 122(3), 871–880 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Harris, K., Montalbán, A.: Boolean Algebra Approximations. (Submitted for publication)

  5. Harris, K., Montalbán, A.: On the n-back-and-forth types of Boolean algebras. Trans. Am. Math. Soc. (to appear)

  6. Hirschfeldt, D., Kach, A.M., Montalbán, A.: A Feiner Look at the Intermediate Degrees. (In preparation)

  7. Kach, A.M., Miller, J.S.: Embeddings of Computable Linear Orders. (In preparation)

  8. Knight, J.F., Stob, M.: Computable Boolean algebras. J. Symb. Logic 65(4), 1605–1623 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lerman, M.: On recursive linear orderings. Logic year 1979–80. In: Proc. Seminars and Conf. Math. Logic, Univ. Connecticut, Storrs, Conn., 1979/80. Springer, Berlin (1981)

    Google Scholar 

  10. Miller, R.: The \(\Delta^0_2\)-spectrum of a linear order. J. Symb. Logic 66(2), 470–486 (2001)

    Article  MATH  Google Scholar 

  11. Montalbán, A.: Notes on the jump of a structure. Mathematical Theory and Computational Practice 372–378 (2009)

  12. Rosenstein, J.G.: Linear orderings. In: Pure and Applied Mathematics, vol. 98. Academic, New York (1982)

    Google Scholar 

  13. Spector, M.: Recursive well orderings. J. Symb. Logic 20, 151–163 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  14. Thurber, J.J.: Every \({\rm low}\sb 2\) Boolean algebra has a recursive copy. Proc. Am. Math. Soc. 123(12), 3859–3866 (1995)

    MathSciNet  MATH  Google Scholar 

  15. Watnick, R.: A generalization of Tennenbaum’s theorem on effectively finite recursive linear orderings. J. Symb. Logic 49(2), 563–569 (1984)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Asher M. Kach.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kach, A.M., Montalbán, A. Cuts of Linear Orders. Order 28, 593–600 (2011). https://doi.org/10.1007/s11083-010-9194-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-010-9194-9

Keywords

Mathematics Subject Classifications (2010)

Navigation