$p$-points in iterated forcing extensions
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- by Judy Roitman
- Proc. Amer. Math. Soc. 69 (1978), 314-318
- DOI: https://doi.org/10.1090/S0002-9939-1978-0469759-X
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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
- D. Booth, Countably indexed ultrafilters, Ph. D. thesis, Univ. of Wisconsin, Madison, Wis., 1969.
J. Ketonen, Some problems about ultrafilters (unpublished).
- Kenneth Kunen, Some points in $\beta N$, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 3, 385–398. MR 427070, DOI 10.1017/S0305004100053032
- Richard Laver, On the consistency of Borel’s conjecture, Acta Math. 137 (1976), no. 3-4, 151–169. MR 422027, DOI 10.1007/BF02392416
- A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), no. 1, 59–111. MR 491197, DOI 10.1016/0003-4843(77)90006-7
- Walter Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409–419. MR 80902
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- 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