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ISSN 1088-6826(online) ISSN 0002-9939(print)



Zapping small filters

Author: Claude Laflamme
Journal: Proc. Amer. Math. Soc. 114 (1992), 535-544
MSC: Primary 03E35; Secondary 03E05, 04A20
MathSciNet review: 1068126
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Abstract: We show two methods for diagonalizing filters of the form $ {F_\sigma }$, first without adding an unbounded real, the other while preserving $ P$-points; the interest lies in an attempt at destroying maximal almost disjoint families with least damage.

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

  • [1] S. Shelah, Vive la différence, no. 326, October 1990.
  • [2] A. Blass and S. Shelah, There may be simple $ {P_{{\aleph _1}}}$, and $ {P_{{\aleph _2}}}$ points and the Rudin-Keisler ordering may be downward directed, Ann. Pure Appl. Logic 83 (1987), 213-243. MR 879489 (88e:03073)
  • [3] K. Kunen, Set theory, North-Holland, Amsterdam, 1980. MR 597342 (82f:03001)
  • [4] C. Laflamme, Forcing with filters and complete combinatorics, Ann. Pure Appl. Logic 42 (1989), 125-163. MR 996504 (90d:03104)
  • [5] M. Talagrand, Compacts de fonctions mesurables et filtres non mesurables, Studia Math. 67 (1980), 13-43. MR 579439 (82e:28009)
  • [6] J. Vaughan, Small uncountable cardinals and topology, preprint, 1989. MR 1078647

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Article copyright: © Copyright 1992 American Mathematical Society

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