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The -spectrum of a linear order

Published online by Cambridge University Press:  12 March 2014

Russell Miller
Russell Miller*
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA, E-mail: russell@math.cornell.edu
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Abstract

Slaman and Wehner have constructed structures which distinguish the computable Turing degree 0 from the noncomputable degrees, in the sense that the spectrum of each structure consists precisely of the noncomputable degrees. Downey has asked if this can be done for an ordinary type of structure such as a linear order. We show that there exists a linear order whose spectrum includes every noncomputable degree, but not 0. Since our argument requires the technique of permitting below a set, we include a detailed explantion of the mechanics and intuition behind this type of permitting.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001 , pp. 470 - 486
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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