A basis theorem for perfect sets

Bulletin of Symbolic Logic 4 (2):204-209 (1998)
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Abstract

We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair $M\subset N$ of models of set theory implying that every perfect set in N has an element in N which is not in M

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reprint Groszek, Marcia J.; Slaman, Theodore A. (1998) "A Basis Theorem For Perfect Sets, By, Pages 204 -- 209". Bulletin of Symbolic Logic 4(2):204-209

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On effective σ‐boundedness and σ‐compactness.Vladimir Kanovei & Vassily Lyubetsky - 2013 - Mathematical Logic Quarterly 59 (3):147-166.
The Nonstationary Ideal in the Pmax Extension.Paul B. Larson - 2007 - Journal of Symbolic Logic 72 (1):138 - 158.
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References found in this work

What is Cantor's Continuum Problem?Kurt Gödel - 1947 - The American Mathematical Monthly 54 (9):515--525.
[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
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Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
One hundred and two problems in mathematical logic.Harvey Friedman - 1975 - Journal of Symbolic Logic 40 (2):113-129.

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