Two remarks about analytic sets

  • Fons van Engelen
  • Kenneth Kunen
  • Arnold W. Miller
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1401)


In this paper we give two results about analytic sets. The first is a counterexample to a problem of Fremlin. We show that there exists ω1 compact subsets of a Borel set with the property that no σ-compact subset of the Borel set covers them. In the second section we prove that for any analytic subset A of the plane either A can be covered by countably many lines or A contains a perfect subset P which does not have three collinear points.


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    A. S. Kechris and D. A. Martin, Infinite games and effective descriptive set theory, in Analytic Sets, ed. by C. A. Rogers et al, Academic Press, (1980), 404–470.Google Scholar
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    D. H. Fremlin, Consequences of Martin’s Axiom, Cambridge University Press, (1984).Google Scholar
  3. [3]
    R. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Annals of Mathematics, 92(1970), 1–56.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Fons van Engelen
    • 1
  • Kenneth Kunen
    • 2
  • Arnold W. Miller
    • 3
  1. 1.Vrÿe Universiteit Subfaculteit WiskundeAmsterdamThe Netherlands
  2. 2.Department of MathematicsUniversity of WisconsinMadison
  3. 3.Department of MathematicsUniversity of WisconsinMadison

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