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Proceedings of the American Mathematical Society

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A note on $ \sb 2{\rm sc}({\bf E}\sb 1)$


Author: Rana Barua
Journal: Proc. Amer. Math. Soc. 103 (1988), 921-925
MSC: Primary 03D65; Secondary 03D55
DOI: https://doi.org/10.1090/S0002-9939-1988-0947683-X
MathSciNet review: 947683
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Abstract: We exhibit a set of reals recursive in $ {{\mathbf{E}}_1}$ which is not in $ \mathcal{C}$, the smallest $ \sigma $-field containing analytic sets and closed under operation $ \mathcal{A}$. As a consequence, a conjecture of Hinman is shown to be false.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947683-X
Keywords: Recursion in type-2 objects, effective hierarchy, $ C$-sets, operation $ \mathcal{A}$, $ \delta - s$ operations, universal sets, games
Article copyright: © Copyright 1988 American Mathematical Society

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