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Blowing up the power set of the least measurable

Published online by Cambridge University Press:  12 March 2014

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/

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Apter, A., Forcing the least measurable to violate GCH, Mathematical Logic Quarterly, vol. 45 (1999), pp. 551560.CrossRefGoogle Scholar
[2]Apter, A. and Cummings, J., Identity crises and strong compactness, this Journal, vol. 65 (2000), pp. 18951910.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. 139.CrossRefGoogle Scholar
[4]Gitik, M., Changing cofinalities and the non-stationary ideal, Israel Journal of Mathematics, vol. 56 (1986), pp. 280314.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. 209234.CrossRefGoogle Scholar
[6]Gitik, M., A club of former regulars, this Journal, vol. 64 (1999), pp. 112.Google Scholar
[7]Hamkins, J., The lottery preparation, Annals of Pure and Applied Logic, vol. 101 (2000), pp. 103146.CrossRefGoogle Scholar
[8]Levinski, J.-P., Filters and large cardinals, Annals of Pure and Applied Logic, vol. 72 (1995), pp. 177212.CrossRefGoogle Scholar
[9]Mitchell, W., Sets constructible from sequences of ultrafilters, this Journal, vol. 39 (1974), pp. 5766.Google Scholar
[10]Mitchell, W., Sets constructed from sequences of measures: revisited, this Journal, vol. 48 (1983), pp. 600609.Google Scholar
[11]Mitchell, W., The core model for sequences of measures I, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 95 (1984), pp. 229260.CrossRefGoogle Scholar