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Cardinal arithmetic and $ \aleph \sb{1}$-Borel sets


Author: Juris Steprāns
Journal: Proc. Amer. Math. Soc. 84 (1982), 121-126
MSC: Primary 03E35; Secondary 03E15, 03E50
DOI: https://doi.org/10.1090/S0002-9939-1982-0633292-3
MathSciNet review: 633292
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Abstract: It is shown to be consistent with $ {2^{{\aleph _0}}} > {\aleph _1}$ that the smallest $ {\aleph _2}$-complete Boolean subalgebra of $ \mathcal{P}({\mathbf{R}})$ containing all closed sets is $ \mathcal{P}({\mathbf{R}})$. Some related results are also proved.


References [Enhancements On Off] (What's this?)

  • [1] J. E. Baumgartner, Notes on forcing, Cambridge Summer School, 1978.
  • [2] Murray Bell and Kenneth Kunen, On the PI character of ultrafilters, C. R. Math. Rep. Acad. Sci. Canada 3 (1981), no. 6, 351–356. MR 642449
  • [3] F. Hausdorff, Summen von $ {\aleph _1}$-Mengen, Fund. Math. 26 (1936), 241-255.
  • [4] Thomas Jech, Set theory, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. MR 506523
  • [5] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 0270904, https://doi.org/10.1016/0003-4843(70)90009-4
  • [6] K. L. Prikry, Private letter to F.D. Tall.
  • [7] W. Sierpinski, Sur quelques propriétés des ensembles projectifs, C. R. Acad. Sci. Paris 185 (1927), 833-835.
  • [8] F. D. Tall, Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Dissertationes Math. (Rozprawy Mat.) 148 (1977), 53. MR 0454913

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0633292-3
Article copyright: © Copyright 1982 American Mathematical Society