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η-representation of sets and degrees

  • Kenneth Harris (a1)

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.

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[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.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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