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.
Research partially supported by the Netherlands organization for the advancement of pure research
Research partially supported by NSF grant MCS-8401711
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References
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.
D. H. Fremlin, Consequences of Martin’s Axiom, Cambridge University Press, (1984).
R. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Annals of Mathematics, 92(1970), 1–56.
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© 1989 Springer-Verlag
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van Engelen, F., Kunen, K., Miller, A.W. (1989). Two remarks about analytic sets. In: Steprāns, J., Watson, S. (eds) Set Theory and its Applications. Lecture Notes in Mathematics, vol 1401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097332
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DOI: https://doi.org/10.1007/BFb0097332
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