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Degree spectra of intrinsically c.e. relations

Published online by Cambridge University Press:  12 March 2014

Denis R. Hirschfeldt
Denis R. Hirschfeldt*
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
*
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA, E-mail: drh@math.uchicago.edu
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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 α ∈ ω ∪ {ω} then for any α-c.e. degree a > 0 there exists an intrinsically α-c.e. relation on the domain of a computable structure whose degree spectrum {0, a}. All of these results also hold for m-degree spectra of relations.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001 , pp. 441 - 469
Copyright
Copyright © Association for Symbolic Logic 2001

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