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)



There are no $ Q$-points in Laver's model for the Borel conjecture

Author: Arnold W. Miller
Journal: Proc. Amer. Math. Soc. 78 (1980), 103-106
MSC: Primary 03E35; Secondary 03E05
MathSciNet review: 548093
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that it is consistent with ZFC that no nonprincipal ultrafilter on $ \omega $ is a Q-point (also called a rare ultrafilter).

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

  • [C] Gustave Choquet, Deux classes remarquables d’ultrafiltres sur N, Bull. Sci. Math. (2) 92 (1968), 143–153 (French). MR 0236860
  • [Ke] Jussi Ketonen, On the existence of 𝑃-points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), no. 2, 91–94. MR 0433387
  • [Ku1] Kenneth Kunen, Some points in 𝛽𝑁, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 3, 385–398. MR 0427070
  • [Ku2] -, P pt's in random real extensions (to appear).
  • [L] Richard Laver, On the consistency of Borel’s conjecture, Acta Math. 137 (1976), no. 3-4, 151–169. MR 0422027
  • [M1] A. R. D. Mathias, A remark on rare filters, Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdös on his 60th birthday), Vol. III, North-Holland, Amsterdam, 1975, pp. 1095–1097. Colloq. Math. Soc. János Bolyai, Vol. 10. MR 0373898
  • [M2] A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), no. 1, 59–111. MR 0491197
  • [M3] -, 0# and the P-point problem (to appear).
  • [R] J. Roitman, P-pts in iterated forcing extensions (to appear).
  • [W] Edward L. Wimmers, The Shelah 𝑃-point independence theorem, Israel J. Math. 43 (1982), no. 1, 28–48. MR 728877, 10.1007/BF02761683

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E35, 03E05

Retrieve articles in all journals with MSC: 03E35, 03E05

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society