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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Recursiveness in $ P^1_1$ paths through $ \mathcal{O}$


Author: Harvey Friedman
Journal: Proc. Amer. Math. Soc. 54 (1976), 311-315
DOI: https://doi.org/10.1090/S0002-9939-1976-0398812-2
MathSciNet review: 0398812
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Abstract: Kleene's $ \mathcal{O}$ is recursive in some $ \Pi _1^1$ path through $ \mathcal{O}$. If every hyp set is recursive in a given $ \Pi _1^1$ set, then $ \mathcal{O}$ is recursive in its triple jump.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0398812-2
Keywords: Kleene's $ \mathcal{O}$, $ \Pi _1^1$ path through $ \mathcal{O}$, hyperarithmetic, recursive
Article copyright: © Copyright 1976 American Mathematical Society

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