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Proceedings of the American Mathematical Society

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$ p$-points in iterated forcing extensions


Author: Judy Roitman
Journal: Proc. Amer. Math. Soc. 69 (1978), 314-318
MSC: Primary 02K05
DOI: https://doi.org/10.1090/S0002-9939-1978-0469759-X
MathSciNet review: 0469759
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Abstract: Selective ultrafilters exist in direct iterated ccc extensions whose length has uncountable cofinality, as do p-points which are not selective. Nonselective p-points also exist e.g. in an iterated Laver or Mathias extension of length $ {\omega _2}$ over a model of CH.


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

  • [B] D. Booth, Countably indexed ultrafilters, Ph. D. thesis, Univ. of Wisconsin, Madison, Wis., 1969.
  • [Ke] J. Ketonen, Some problems about ultrafilters (unpublished).
  • [Ku] K. Kunen, Some points in $ \beta N$, Proc. Cambridge Philos. Soc. (1976), 385-398. MR 0427070 (55:106)
  • [L] R. Laver, On the Borel conjecture, Acta Math. 137 (1976). MR 0422027 (54:10019)
  • [M] A. Mathias, Happy families (to appear). MR 0491197 (58:10462)
  • [R] W. Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409-419. MR 0080902 (18:324d)

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DOI: https://doi.org/10.1090/S0002-9939-1978-0469759-X
Article copyright: © Copyright 1978 American Mathematical Society

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