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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the jump of an $ \alpha $-recursively enumerable set


Author: Richard A. Shore
Journal: Trans. Amer. Math. Soc. 217 (1976), 351-363
MSC: Primary 02F27
DOI: https://doi.org/10.1090/S0002-9947-1976-0424544-2
MathSciNet review: 0424544
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Abstract: We discuss the proper definition of the jump operator in $ \alpha $-recursion theory and prove a sample theorem: There is an incomplete $ \alpha $-r.e. set with jump $ 0''$ unless there is precisely one nonhyperregular $ \alpha $-r.e. degree. Thus we have a theorem in the first order language of Turing degrees with the jump which fails to generalize to all admissible $ \alpha $.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0424544-2
Keywords: $ \alpha $-recursion theory, admissible ordinals, $ \alpha $-recursively enumerable, $ \alpha $-degree, $ \alpha $-jump, priority arguments
Article copyright: © Copyright 1976 American Mathematical Society

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