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Dual Borel Conjecture and Cohen reals

  • Tomek Bartoszynski (a1) and Saharon Shelah (a2)

We construct a model of ZFC satisfying the Dual Borel Conjecture in which there is a set of size ℵ1 that does not have measure zero.

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[2]Timothy J. Carlson , Strong measure zero and strongly meager sets, Proceedings of the American Mathematical Society, vol. 118 (1993), no. 2, pp. 577586.

[3]Haim Judah and Saharon Shelah , MA(σ-centered): Cohen reals, strong measure zero sets and strongly meager sets, Israel Journal of Mathematics, vol. 68 (1989), no. 1, pp. 117.

[4]Haim Judah , Saharon Shelah , and W. H. Woodin , The Borel conjecture, Annals of Pure and Applied Logic, vol. 50 (1990), no. 3, pp. 255269.

[5]Richard Laver , On the consistency of Borel's conjecture, Acta Mathematica, vol. 137 (1976), no. 3-4, pp. 151169.

[6]G. Lorentz , On a problem of additive number theory, Proceedings of the American Mathematical Society, vol. 5 (1954), pp. 838841.

[9]Saharon Shelah , Proper and improper forcing, Perspectives in Logic, Springer-Verlag, 1998.

[10]Saharon Shelah , Non-Cohen oracle c.c.c., Journal of Applied Analysis, vol. 12 (2006), pp. 117.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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