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Jumping through the transfinite: the master code hierarchy of Turing degrees1

Published online by Cambridge University Press:  12 March 2014

Harold T. Hodes
Harold T. Hodes*
Affiliation:
Cornell Universrty, Ithaca, New York 14853
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Abstract

Where a is a Turing degree and ξ is an ordinal < (ℵ1)L1, the result of performing ξ jumps on a, a(ξ), is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through (ℵ1)L1 of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 45 , Issue 2 , June 1980 , pp. 204 - 220
Copyright
Copyright © Association for Symbolic Logic 1980

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Footnotes

*

Thanks to the referee for finding several major and many minor errors. Special thanks to F. Abramson for suggesting the use of modified Steel conditions in the proofs of Lemmas 1 and 2 under Case 3. Writing of this paper was in part supported by a Fellowship from the Mellon Foundation.

References

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