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Some remarks on changing cofinalities

Published online by Cambridge University Press:  12 March 2014

Keith J. Devlin
Keith J. Devlin*
Affiliation:
University of Manchester, Manchester M13 9PL, England
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Abstract

In [2], Prikry showed that if κ is a weakly inaccessible cardinal which carries a Rowbottom filter, then there is a Boolean extension of V (the universe), having the same cardinals as V, in which cf(κ) = ω. In this note, we obtain necessary and sufficient conditions which a filter D on κ must possess in order that this may be done.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 39 , Issue 1 , March 1974 , pp. 27 - 30
Copyright
Copyright © Association for Symbolic Logic 1974

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References

REFERENCES

[1]Devlin, K. J., Some weak versions of large cardinal axioms, Annals of Mathematical Logic, vol. 5 (1973), pp. 271–325.CrossRefGoogle Scholar
[2]Prikry, K. L., Changing measurable into accessible cardinals, Rozprawy Matematyczne, vol. 68 (1970), pp. 5–52.Google Scholar
[3]Scott, D. and Solovay, R., Boolean valued models for set theory, Proceedings of the 1967 Summer Institute on Set Theory.Google Scholar
[4]Shoenfield, J. R., Unramified forcing, Proceedings of Symposia in Pure Mathematics (University of California, Los Angeles, 1967), Vol. 13, Part I, American Mathematical Society, 1971, Providence, R.I., pp. 357–381.Google Scholar