Cardinal arithmetic and $\aleph _{1}$-Borel sets
HTML articles powered by AMS MathViewer
- by Juris Steprāns PDF
- Proc. Amer. Math. Soc. 84 (1982), 121-126 Request permission
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
-
J. E. Baumgartner, Notes on forcing, Cambridge Summer School, 1978.
- 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 F. Hausdorff, Summen von ${\aleph _1}$-Mengen, Fund. Math. 26 (1936), 241-255.
- Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
- D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4 K. L. Prikry, Private letter to F.D. Tall. W. Sierpinski, Sur quelques propriétés des ensembles projectifs, C. R. Acad. Sci. Paris 185 (1927), 833-835.
- 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 454913
Additional Information
- © Copyright 1982 American Mathematical Society
- 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