There are no -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 is a *Q*-point (also called a rare ultrafilter).

**[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

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

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

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1980-0548093-2

Article copyright:
© Copyright 1980
American Mathematical Society