Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



$ p$-points in iterated forcing extensions

Author: Judy Roitman
Journal: Proc. Amer. Math. Soc. 69 (1978), 314-318
MSC: Primary 02K05
MathSciNet review: 0469759
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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  • [Ke] J. Ketonen, Some problems about ultrafilters (unpublished).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] Kenneth Kunen, Some points in 𝛽𝑁, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 3, 385–398. MR 0427070
  • [L] Richard Laver, On the consistency of Borel’s conjecture, Acta Math. 137 (1976), no. 3-4, 151–169. MR 0422027
  • [M] A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), no. 1, 59–111. MR 0491197
  • [R] Walter Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409–419. MR 0080902

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02K05

Retrieve articles in all journals with MSC: 02K05

Additional Information

Article copyright: © Copyright 1978 American Mathematical Society