-points in random universes

Author:
Paul E. Cohen

Journal:
Proc. Amer. Math. Soc. **74** (1979), 318-321

MSC:
Primary 54D40; Secondary 03E05, 03E40

DOI:
https://doi.org/10.1090/S0002-9939-1979-0524309-5

MathSciNet review:
524309

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A pathway is defined as an increasing sequence of subsets of which satisfy certain closure and boundedness properties. The existence of a pathway is shown to imply the existence of a *P*-point in . Pathways are shown to exist in any random extension of a model of .

**[1]**A. Blass,*The Rudin-Keisler ordering of P-points*, Trans. Amer. Math. Soc.**179**(1973), 145-166. MR**0354350 (50:6830)****[2]**P. Halmos,*Measure theory*, Van Nostrand, New York, 1950. MR**0033869 (11:504d)****[3]**T. Jech,*Lectures in set theory with particular emphasis on the method of forcing*, Lecture Notes in Math., Vol. 217, Springer, Berlin, 1971. MR**0321738 (48:105)****[4]**J. Ketonen,*On the existence of P-points in the Stone-Čech compactification of the integers*, Fund. Math.**42**(1976), 91-94. MR**0433387 (55:6363)****[5]**K. Kunen,*P-points in random real extensions*(unpublished note).**[6]**A. Mathias,*Happy families*(to appear). MR**0491197 (58:10462)****[7]**M. Rudin,*Lectures on set theoretic topology*, CBMS Regional Conf. Ser. in Math., no. 23, Amer. Math. Soc., Providence, R. I., 1975. MR**0367886 (51:4128)****[8]**S. Shelah,*On P-points*,*and other results in general topology*, Notices Amer. Math. Soc.**25**(1978), A-365, Abstract #87T-G49.**[9]**R. Solovay,*A model of set-theory in which every set of reals is Lebesgue measurable*, Ann. of Math. (2)**92**(1970), 1-56. MR**0265151 (42:64)****[10]**G. Takeuti and W. Zaring,*Axiomatic set theory*, Springer, Berlin, 1973. MR**0416914 (54:4977)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54D40,
03E05,
03E40

Retrieve articles in all journals with MSC: 54D40, 03E05, 03E40

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0524309-5

Keywords:
Stone-Cech compactification,
*P*-points,
random forcing

Article copyright:
© Copyright 1979
American Mathematical Society