Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T14:49:38.349Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniformization principles

Published online by Cambridge University Press:  12 March 2014

Alan H. Mekler  and
Saharon Shelah
Alan H. Mekler
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

It is consistent that for many cardinals λ there is a family of at least λ+ unbounded subsets of λ which have uniformization properties. In particular if it is consistent that a supercompact cardinal exists, then it is consistent that ℵω has such a family. We have applications to point set topology, Whitehead groups and reconstructing separable abelian p-groups from their socles.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 2 , June 1989 , pp. 441 - 459
Copyright
Copyright © Association for Symbolic Logic 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[CG]Corner, A. L. S. and Göbel, R., Prescribing endomorphism algebras, a unified treatment, Proceedings of the London Mathematical Society, ser. 3, vol. 50 (1985), pp. 447–479.CrossRefGoogle Scholar
[DJ]Devlin, K. and Johnsbråten, H., The Souslin problem, Lecture Notes in Mathematics, vol. 405, Springer-Verlag, Berlin, 1974.CrossRefGoogle Scholar
[DS]Devlin, K. and Shelah, S., A weak version of ◊ which follows from , Israel Journal of Mathematics, vol. 29 (1978), pp. 239–247.CrossRefGoogle Scholar
[KM]Kanamori, A. and Magidor, M., The evolution of large cardinal axioms in set theory, Higher set theory, Lecture Notes in Mathematics, vol. 669, Springer-Verlag, Berlin, 1978, pp. 99–275.CrossRefGoogle Scholar
[L]Laver, R., Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol. 29 (1978), pp. 385–388.CrossRefGoogle Scholar
[M1]Magidor, M., On the singular cardinals problem. I, Israel Journal of Mathematics, vol. 28(1977), pp. 1–31.CrossRefGoogle Scholar
[M2]Magidor, M., Changing cofinality of cardinals, Fundamenta Mathematicae, vol. 99 (1978), pp. 61–71.CrossRefGoogle Scholar
[MaSo]Martin, D. and Solovay, R., Internal Cohen extensions, Annals of Mathematical Logic, vol. 2 (1970), pp. 143–178.CrossRefGoogle Scholar
[MS]Mekler, A. H. and Shelah, S., ω-elongations and Crawley's problem, Pacific Journal of Mathematics, vol. 121 (1986), pp. 121–132.CrossRefGoogle Scholar
[S0]Shelah, S., Whitehead groups may not be free even assuming CH. I, Israel Journal of Mathematics, vol. 28 (1977), pp. 193–203.CrossRefGoogle Scholar
[S1]Shelah, S., Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978.Google Scholar
[S2]Shelah, S., On uncountable abelian groups, Israel Journal of Mathematics, vol. 32 (1979), pp. 311–330.CrossRefGoogle Scholar
[S3]Shelah, S., Whitehead groups may not be free even assuming CH. II, Israel Journal of Mathematics, vol. 35 (1980), pp. 257–285.CrossRefGoogle Scholar
[S4]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1980.Google Scholar
[S5]Shelah, S., Reconstructing p-groups from their socles, Israel Journal of Mathematics, vol. 60 (1987), pp. 146–166.CrossRefGoogle Scholar