$\Pi _{2}^{1}$ 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 | References | Similar Articles | Additional Information

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