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)

Abstract

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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References

  1. [1]
    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
  2. [2]
    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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