On the jump of an -recursively enumerable set

Author:
Richard A. Shore

Journal:
Trans. Amer. Math. Soc. **217** (1976), 351-363

MSC:
Primary 02F27

MathSciNet review:
0424544

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Abstract: We discuss the proper definition of the jump operator in -recursion theory and prove a sample theorem: *There is an incomplete* -*r.e. set with jump* *unless there is precisely one nonhyperregular* -*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 .

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DOI:
https://doi.org/10.1090/S0002-9947-1976-0424544-2

Keywords:
-recursion theory,
admissible ordinals,
-recursively enumerable,
-degree,
-jump,
priority arguments

Article copyright:
© Copyright 1976
American Mathematical Society