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A Basis Theorem for Perfect Sets

  • Marcia J. Groszek (a1) and Theodore A. Slaman (a2)

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 MN 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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[2[ K. Gödel , What is Cantor's continuum problem?, American Mathematical Monthly, vol. 54 (1947), pp. 515527.

[6[ A. R. D. Mathias , Surrealist landscape with figures (a survey of recent results in set theory), Periodica Mathematica Hungarica, vol. 10 (1979), pp. 109175.

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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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