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A Basis Theorem for Perfect Sets

Published online by Cambridge University Press:  15 January 2014

Marcia J. Groszek  and
Theodore A. Slaman
Marcia J. Groszek
Affiliation:
Department of Mathematics and Computer Science, Dartmouth College, Hanover, NH 03755, USAE-mail: [email protected]
Theodore A. Slaman
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USAE-mail: [email protected]
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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 ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 4 , Issue 2 , June 1998 , pp. 204 - 209
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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