Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T19:02:51.936Z Has data issue: false hasContentIssue false
  • English
  • Français

Blowing up the power set of the least measurable

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter  and
James Cummings
Arthur W. Apter
Affiliation:
Department of Mathematics, Baruch College of Cuny, New York NY 10010, USA, E-mail: [email protected], URL: http://math.baruch.cuny.edu/~apter
James Cummings
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA 15213, USA, E-mail: [email protected], URL: http://www.math.cmu.edu/users/jcumming/
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove some results related to the problem of blowing up the power set of the least measurable cardinal. Our forcing results improve those of [1] by using the optimal hypothesis.

Keywords

Measurable cardinalGCHReverse Easton forcinginner model
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 915 - 923
Copyright
Copyright © Association for Symbolic Logic 2002

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]Apter, A., Forcing the least measurable to violate GCH, Mathematical Logic Quarterly, vol. 45 (1999), pp. 551–560.CrossRefGoogle Scholar
[2]Apter, A. and Cummings, J., Identity crises and strong compactness, this Journal, vol. 65 (2000), pp. 1895–1910.Google Scholar
[3]Cummings, J., A model in which GCH holds at successors but fails at limits, Transactions of the American Mathematical Society, vol. 329 (1992), pp. 1–39.CrossRefGoogle Scholar
[4]Gitik, M., Changing cofinalities and the non-stationary ideal, Israel Journal of Mathematics, vol. 56 (1986), pp. 280–314.CrossRefGoogle Scholar
[5]Gitik, M., The negation of the singular cardinal hypothesis from o(κ) = κ++, Annals of Pure and Applied Logic, vol. 43 (1989), pp. 209–234.CrossRefGoogle Scholar
[6]Gitik, M., A club of former regulars, this Journal, vol. 64 (1999), pp. 1–12.Google Scholar
[7]Hamkins, J., The lottery preparation, Annals of Pure and Applied Logic, vol. 101 (2000), pp. 103–146.CrossRefGoogle Scholar
[8]Levinski, J.-P., Filters and large cardinals, Annals of Pure and Applied Logic, vol. 72 (1995), pp. 177–212.CrossRefGoogle Scholar
[9]Mitchell, W., Sets constructible from sequences of ultrafilters, this Journal, vol. 39 (1974), pp. 57–66.Google Scholar
[10]Mitchell, W., Sets constructed from sequences of measures: revisited, this Journal, vol. 48 (1983), pp. 600–609.Google Scholar
[11]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