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On closed unbounded sets consisting of former regulars

Published online by Cambridge University Press:  12 March 2014

Moti Gitik
Moti Gitik*
Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, 69978, Israel, E-mail, gitik@math.tau.ac.il
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Abstract

A method of iteration of Prikry type forcing notions as well as a forcing for adding clubs is presented. It is applied to construct a model with a measurable cardinal containing a club of former regulars, starting with ο(κ) = κ + 1. On the other hand, it is shown that the strength of above is at least

ο(κ) = κ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 1 - 12
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Avraham, U. and Shelah, S., Forcing closed unbounded sets, this Journal, vol. 48 (1983), pp. 643–648.Google Scholar
[2]Gitik, M., Changing cofinalities and the nonstationary ideal, Israel Journal of Mathematics, vol. 56 (1986), no. 3, pp. 280–314.CrossRefGoogle Scholar
[3]Gitik, M., On the Mitchell and Rudin-Kiesler orderings of ultrafilters, Annals of Pure and Applied Logic, vol. 39 (1988), pp. 175–197.CrossRefGoogle Scholar
[4]Gitik, M., On measurable cardinals violating GCH, Annals of Pure and Applied Logic, vol. 63 (1993), pp. 227–240.CrossRefGoogle Scholar
[5]Gitik, M. and Shelah, S., On certain indestructibility of strong cardinals and a question of Hajnal, Archive for Mathematical Logic, vol. 28 (1989), pp. 35–42.CrossRefGoogle Scholar
[6]Mitchell, W., How weak is a closed unbounded ultrafilter?, Logic collection 80, North-Holland, 1982, pp. 209–231.Google Scholar
[7]Mitchell, W., The core model for sequences of measures I, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 95 (1984), pp. 229–260.CrossRefGoogle Scholar
[8]Mitchell, W., Applications of the core model for sequences of measures, Transactions of the American Mathematical Society, vol. 299 (1987), pp. 41–58.CrossRefGoogle Scholar