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Transactions of the American Mathematical Society

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

 

 

Hyperarithmetical index sets in recursion theory


Author: Steffen Lempp
Journal: Trans. Amer. Math. Soc. 303 (1987), 559-583
MSC: Primary 03D25; Secondary 03D55
DOI: https://doi.org/10.1090/S0002-9947-1987-0902785-2
MathSciNet review: 902785
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Abstract: We define a family of properties on hyperhypersimple sets and show that they yield index sets at each level of the hyperarithmetical hierarchy. An extension yields a $ \Pi _1^1$-complete index set. We also classify the index set of quasimaximal sets, of coinfinite r.e. sets not having an atomless superset, and of r.e. sets major in a fixed nonrecursive r.e. set.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0902785-2
Article copyright: © Copyright 1987 American Mathematical Society