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Saturated Ideals in Boolean Extensions

Published online by Cambridge University Press:  22 January 2016

Yuzuru Kakuda
Yuzuru Kakuda*
Affiliation:
Nagoya University
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0. Introduction. Let k be an uncountable cardinal, and let λ be a regular cardinal less than k. Let I be a λ-saturated non-trivial ideal on k. Prikry, in his thesis, showed that, in certain Boolean extensions, k has a λ-saturated non-trivial ideal on k.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 48 , December 1972 , pp. 159 - 168
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Kunen, K., Some applications of iterated ultrapowers in set theory. Annals of Math. Logic 1. (1970) 179–227.CrossRefGoogle Scholar
[2] Kunen, K. and Paris, J. B., Boolean extensions and measurable cardinals. Annals Math. Logic Vol. 2 No. 4 (1971) 359–377.CrossRefGoogle Scholar
[3] Levy, A. and Solovay, R., Measurable cardinal and the continuum hypothesis, Israel Journal of Math. Vol. 5 (1967) 234–248.Google Scholar
[4] Scott, D. and Solovay, R., Boolean-valued models for set theory, Proc. 1967. U.C.L.A. Summer Institute, to appear.Google Scholar
[5] Solovay, R., Real-valued measurable cardinals. Proc. of symposia in pure math. Vol. XIII, Part I (1971) 397–428.Google Scholar
[6] Solovay, R., A model of set-theory in which every set of reals is Lebesgue measurable. Annals of Math. 92 (1970) 1–56.CrossRefGoogle Scholar
[7] Solovay, R. and Tennenbaum, S., Iterated Chen extensions and Souslin’s problem. Annals of Math. Vol. 94 No. 2 201–245.Google Scholar
[8] Prikry, K. L., Changing measurable into accessible cardinals. Dissertationes Math. (Rzprawy Mat.) 68 (1970).Google Scholar