Journal of Symbolic Logic

Degree Spectra of Intrinsically C.E. Relations

Denis R. Hirschfeldt

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Abstract

We show that for every c.e. degree a > 0 there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. This result can be extended in two directions. First we show that for every uniformly c.e. collection of sets S there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is the set of degrees of elements of S. Then we show that if $\alpha \in \omega\cup\{\omega \}$ then for any $\alpha$-c.e. degree a > 0 there exists an intrinsically $\alpha$-c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. All of these results also hold for m-degree spectra of relations.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 2 (2001), 441-469.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746453

Mathematical Reviews number (MathSciNet)
MR1833490

Zentralblatt MATH identifier
0988.03065

JSTOR
links.jstor.org

Citation

Hirschfeldt, Denis R. Degree Spectra of Intrinsically C.E. Relations. J. Symbolic Logic 66 (2001), no. 2, 441--469. https://projecteuclid.org/euclid.jsl/1183746453


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