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)



Random reals and Souslin trees

Author: Richard Laver
Journal: Proc. Amer. Math. Soc. 100 (1987), 531-534
MSC: Primary 03E35; Secondary 03E05
MathSciNet review: 891159
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is consistent that there are no Souslin trees in any random extension of $ V$; thus, the continuum can be singular of cofinality $ {\omega _1}$ with Souslin's hypothesis holding.

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

  • [1] J. Baumgartner, J. Malitz, and W. Reinhardt, Embedding trees in the rationals, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 1748-1755. MR 0314621 (47:3172)
  • [2] K. Devlin and H. Johnsbraten, The Souslin problem, Lecture Notes in Math., Vol. 406, Springer-Verlag, Berlin and New York, 1974. MR 0384542 (52:5416)
  • [3] F. Galvin, Chain conditions and products, Fund. Math. 108 (1980), 33-48. MR 585558 (81m:03058)
  • [4] J. Roitman, Adding a random or a Cohen real: topological consequences and the effects on Martin's axiom, Fund. Math. 103 (1979), 47-60. MR 535835 (81h:03098)
  • [5] S. Shelah, Can you take Solovay's inaccessible away?, Israel J. Math. 48 (1984), 1-47. MR 768264 (86g:03082a)
  • [6] R. Solovay, Real valued measurable cardinals, Proc. Sympos. Pure Math., vol. 13, Part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 397-428. MR 0290961 (45:55)
  • [7] R. Solovay and S. Tennenbaum, Iterated Cohen extensions and Souslin's problem, Ann. of Math. 94 (1971), 201-245. MR 0294139 (45:3212)

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 1987 American Mathematical Society

American Mathematical Society