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Measure-theoretic construction of incomparable hyperdegrees

Published online by Cambridge University Press:  12 March 2014

Clifford Spector
Clifford Spector*
Affiliation:
The Ohio State University
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Extract

Kleene-Post [10], Spector [14] and Friedberg [3, 4], have given a number of examples of functions which have incomparable degrees of recursive unsolvability satisfying various additional conditions. Our present purpose is to determine to what extent some of these incomparability theorems can be generalized by substituting for “α. is recursive in β” other relations Q(α, β) such as “α is hyperarithmetical in β” (which we shall think of as “α ≦ β”), and to determine what restrictions, if any, need be imposed on Q. As a consequence of our investigation we shall show that there are incomparable hyperdegrees as defined in [9] and [13].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 23 , Issue 3 , September 1958 , pp. 280 - 288
Copyright
Copyright © Association for Symbolic Logic 1958

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References

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