Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T12:40:44.094Z Has data issue: false hasContentIssue false
  • English
  • Français

On hereditarily countable sets1

Published online by Cambridge University Press:  12 March 2014

Thomas Jech
Thomas Jech*
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania 16802
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown (in ZF) that every hereditarily countable set has rank less than ω2, and that if ℵ1 is singular then there are hereditarily countable sets of all ranks less than ω2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 1 , March 1982 , pp. 43 - 47
Copyright
Copyright © Association for Symbolic Logic 1982

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.)

Footnotes

1

Supported by NSF Grant MCS-7824848.

References

REFERENCES

[1]Gitik, M., All uncountable cardinals can be singular, Ph.D. Thesis, Jerusalem, 1979.Google Scholar
[2]Jech, T., ω1 can be measurable, Israel Journal of Mathematics, vol. 6 (1968), pp. 363–367.CrossRefGoogle Scholar
[3]Magidor, M., On the singular cardinals problem. I, Israel Journal of Mathematics, vol. 28 (1977), pp. 1–31.CrossRefGoogle Scholar
[4]Mitchell, W., Core model for sequences of ultrafilters.Google Scholar
[5]Prikry, K., Changing measurable into accessible cardinals, Dissertationes Mathematicae, vol. 68 (1970), pp. 5–52.Google Scholar