Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 8
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Harris, Charles M. 2015. On limitwise monotonicity and maximal block functions. Computability, Vol. 4, Issue. 2, p. 119.

    Downey, Rod Melnikov, Alexander G. and Ng, Keng Meng 2014. Iterated effective embeddings of abelian p-groups. International Journal of Algebra and Computation, Vol. 24, Issue. 07, p. 1055.

    MELNIKOV, ALEXANDER G. 2014. COMPUTABLE ABELIAN GROUPS. The Bulletin of Symbolic Logic, Vol. 20, Issue. 03, p. 315.

    Bazhenov, N. A. and Tukhbatullina, R. R. 2012. Constructivizability of the boolean algebra $ \mathfrak{B}\left( \omega \right) $ with a distinguished automorphism. Algebra and Logic, Vol. 51, Issue. 5, p. 384.

    Zubkov, M. V. 2011. Strongly η-representable degrees and limitwise monotonic functions. Algebra and Logic, Vol. 50, Issue. 4, p. 346.

    2010. 2009 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '09. Bulletin of Symbolic Logic, Vol. 16, Issue. 01, p. 90.

    Frolov, Andrey N. and Zubkov, Maxim V. 2009. Increasingη-representable degrees. MLQ, Vol. 55, Issue. 6, p. 633.

    Zubkov, M. V. 2009. A theorem on strongly η-representable sets. Russian Mathematics, Vol. 53, Issue. 7, p. 65.


η-representation of sets and degrees

  • Kenneth Harris (a1)
  • DOI:
  • Published online: 01 March 2014

We show that a set has an η-representation in a linear order if and only if it is the range of a 0′-computable limitwise monotonic function. We also construct a Δ3 Turing degree for which no set in that degree has a strong η-representation, answering a question posed by Downey.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[CDK98]R. J. Coles , R. Downey , and B. M. Khoussainov , On initial segments of computable linear orders, Order, vol. 14 (1998), pp. 107–24.

[HMP07]D. Hirschfeldt , R. Miller , and S. Podzorov , Order-computable sets, The Notre Dame Journal of Formal Logic, vol. 48 (2007), no. 3, pp. 317347.

[Ler81]Manuel Lerman , On recursive linear orders, Logic year 1979-80 (M. Lerman , J. H. Schmerl , and R. I. Soare , editors), Lecture Notes in Mathematics, vol. 859, 1981, pp. 132142.

[Soa87]R. I. Soare , Recursively enumerable sets and degrees, Perspectives in Mathematics, Springer-Verlag, 1987.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *