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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
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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

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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