A large $\Pi ^ 1_ 2$ set, absolute for set forcings
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- by Sy D. Friedman PDF
- Proc. Amer. Math. Soc. 122 (1994), 253-256 Request permission
Abstract:
We show how to obtain, by class-forcing over L, a set of reals X which is large in $L(X)$ and has a $\Pi _2^1$ definition valid in all set-generic extensions of $L(X)$. As a consequence we show that it is consistent for the Perfect Set Property to hold for $\Sigma _2^1$ sets yet fail for some $\Pi _2^1$ set. Also it is consistent for the perfect set property to hold for $\Sigma _2^1$ sets and for there to be a long $\Pi _2^1$ well-ordering. These applications (necessarily) assume the consistency of an inaccessible cardinal.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 253-256
- MSC: Primary 03E15; Secondary 03E35
- DOI: https://doi.org/10.1090/S0002-9939-1994-1231297-3
- MathSciNet review: 1231297