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Proceedings of the American Mathematical Society

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

 
 

 

$\Pi _{2}^{1}$ sets and $\Pi _{2}^{1}$ 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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Keywords: Strongly <!– MATH $\Delta _n^1$ –> <IMG WIDTH="33" HEIGHT="43" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$\Delta _n^1$"> well ordering, <IMG WIDTH="30" HEIGHT="43" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\Pi _2^1$"> singletons, constructible reals
Article copyright: © Copyright 1975 American Mathematical Society