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On initial segments of hyperdegrees1

Published online by Cambridge University Press:  12 March 2014

S. K. Thomason
S. K. Thomason*
Affiliation:
Simon Fraser University
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Extract

An initial segment of hyperdegrees is a set S of hyperdegrees such that whenever h ∈ S and k ≦ h then k ∈ S. The main results of this paper affirm the existence of initial segments having certain order types. In particular, if L is a finite distributive lattice then L is isomorphic to an initial segment of hyperdegrees [Theorem 1]; as a consequence the elementary theory of the ordering of hyperdegrees is recursively undecidable [Corollary 1].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 2 , June 1970 , pp. 189 - 197
Copyright
Copyright © Association for Symbolic Logic 1970

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Footnotes

1

This paper reports research supported in part by the National Research Council of Canada, Grant #A-4065.

References

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