Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-08T18:14:49.932Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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.)

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