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Measurability and degrees of strong compactness1

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter
Arthur W. Apter*
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
*
University of Miami, Coral Gables, Florida 33124
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Abstract

We prove, relative to suitable hypotheses, that it is consistent for there to be unboundedly many measurable cardinals each of which possesses a large degree of strong compactness, and that it is consistent to assume that the least measurable is partially strongly compact and that the second measurable is strongly compact. These results partially answer questions of Magidor on the relationship of strong compactness to measurability.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 2 , June 1981 , pp. 249 - 254
Copyright
Copyright © Association for Symbolic Logic 1981

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Footnotes

1

The results obtained in this paper form a portion of the author's doctoral dissertation written at M.I.T. under Professor E. M. Kleinberg, to whom the author is indebted for his aid and encouragement.

References

REFERENCES

[1]Apter, A., Changing cofinalities and infinite exponents, this Journal, vol. 46 (1981), pp. 89–95.Google Scholar
[2]Apter, A., Large cardinals and relative consistency results, Doctoral Dissertation, Massachusetts Institute of Technology, 1978.Google Scholar
[3]Keisler, H.J. and Tarski, A., From accessible to inaccessible cardinals, Fund amenta Mathematicae, vol. 53 (1964), pp. 225–308.CrossRefGoogle Scholar
[4]Levy, A. and Solovay, R., Measurable cardinals and the continuum hypothesis, Israel Journal of Mathematics, vol. 5 (1967), pp. 234–248.CrossRefGoogle Scholar
[5]Magidor, M., HOW large is the first strongly compact cardinal?, Annals of Mathematical Logic, vol. 10 (1976), pp. 35–57.CrossRefGoogle Scholar
[6]Menas, T.K., On strong compactness and supercompactness, Doctoral Dissertation, University of California, Berkeley, 1973.Google Scholar
[7]Silver, J., Large cardinals and GCH (to appear).Google Scholar
[8]Solovay, R., Strongly compact cardinals and the GCH, Tarski Symposium, Proceedings of Symposia in Pure Mathematics, vol. 25, American Mathematical Society, Providence, Rhode Island, 1974, pp. 365–372.Google Scholar
[9]Solovay, R., Reinhardt, W. and Kanamori, A., Strong axioms of infinity and elementary embeddings, Annals of Mathematical Logic, vol. 13 (1978), pp. 73–116.CrossRefGoogle Scholar
[10]Solovay, R. and Tennenbaum, S., Iterated Cohen extensions and Souslin's problem, Annals of Mathematics, vol. 94 (1971), pp. 201–245.CrossRefGoogle Scholar