points in random universes
Author:
Paul E. Cohen
Journal:
Proc. Amer. Math. Soc. 74 (1979), 318321
MSC:
Primary 54D40; Secondary 03E05, 03E40
MathSciNet review:
524309
Fulltext PDF Free Access
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 Ppoint in . Pathways are shown to exist in any random extension of a model of .
 [1]
Andreas
Blass, The RudinKeisler ordering of
𝑃points, Trans. Amer. Math. Soc.
179 (1973),
145–166. MR 0354350
(50 #6830), http://dx.doi.org/10.1090/S00029947197303543506
 [2]
Paul
R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New
York, N. Y., 1950. MR 0033869
(11,504d)
 [3]
Thomas
J. Jech, Lectures in set theory, with particular emphasis on the
method of forcing, Lecture Notes in Mathematics, Vol. 217,
SpringerVerlag, BerlinNew York, 1971. MR 0321738
(48 #105)
 [4]
Jussi
Ketonen, On the existence of 𝑃points in the
StoneČech compactification of integers, Fund. Math.
92 (1976), no. 2, 91–94. MR 0433387
(55 #6363)
 [5]
K. Kunen, Ppoints in random real extensions (unpublished note).
 [6]
A.
R. D. Mathias, Happy families, Ann. Math. Logic
12 (1977), no. 1, 59–111. MR 0491197
(58 #10462)
 [7]
Mary
Ellen Rudin, Lectures on set theoretic topology, Published for
the Conference Board of the Mathematical Sciences by the American
Mathematical Society, Providence, R.I., 1975. Expository lectures from the
CBMS Regional Conference held at the University of Wyoming, Laramie, Wyo.,
August 12–16, 1974; Conference Board of the Mathematical Sciences
Regional Conference Series in Mathematics, No. 23. MR 0367886
(51 #4128)
 [8]
S. Shelah, On Ppoints, and other results in general topology, Notices Amer. Math. Soc. 25 (1978), A365, Abstract #87TG49.
 [9]
Robert
M. Solovay, A model of settheory in which every set of reals is
Lebesgue measurable, Ann. of Math. (2) 92 (1970),
1–56. MR
0265151 (42 #64)
 [10]
Gaisi
Takeuti and Wilson
M. Zaring, Axiomatic set theory, SpringerVerlag, New
YorkBerlin, 1973. With a problem list by Paul E. Cohen; Graduate Texts in
Mathematics, Vol. 8. MR 0416914
(54 #4977)
 [1]
 A. Blass, The RudinKeisler ordering of Ppoints, Trans. Amer. Math. Soc. 179 (1973), 145166. 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 Ppoints in the StoneČech compactification of the integers, Fund. Math. 42 (1976), 9194. MR 0433387 (55:6363)
 [5]
 K. Kunen, Ppoints 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 Ppoints, and other results in general topology, Notices Amer. Math. Soc. 25 (1978), A365, Abstract #87TG49.
 [9]
 R. Solovay, A model of settheory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 156. MR 0265151 (42:64)
 [10]
 G. Takeuti and W. Zaring, Axiomatic set theory, Springer, Berlin, 1973. MR 0416914 (54:4977)
Similar Articles
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:
http://dx.doi.org/10.1090/S00029939197905243095
PII:
S 00029939(1979)05243095
Keywords:
StoneCech compactification,
Ppoints,
random forcing
Article copyright:
© Copyright 1979
American Mathematical Society
