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Proceedings of the American Mathematical Society

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$ \Pi \sb{2}\sp{1}$ sets and $ \Pi \sb{2}\sp{1}$ singletons


Author: Leo Harrington
Journal: Proc. Amer. Math. Soc. 52 (1975), 356-360
MSC: Primary 02K30
DOI: https://doi.org/10.1090/S0002-9939-1975-0373896-5
MathSciNet review: 0373896
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Abstract: The following are equivalent:

(a) every real is constructible;

(b) every nonempty $ \prod _2^1$ set of reals contains a $ \prod _2^1$ singleton. (Implication $ ({\text{a}}) \Rightarrow ({\text{b}})$ is due solely to H. Friedman.)


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0373896-5
Keywords: Strongly $ \Delta _n^1$ well ordering, $ \Pi _2^1$ singletons, constructible reals
Article copyright: © Copyright 1975 American Mathematical Society

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