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The least measurable can be strongly compact and indestructible

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter  and
Moti Gitik
Arthur W. Apter
Affiliation:
Department of Mathematics, Baruch College of Cuny, New York, New York 10010., USA. E-mail: awabb@cunyvm.cuny.edu
Moti Gitik
Affiliation:
Department of Mathematics, Tel Aviv University, 69978 Tel Aviv, Israel
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Abstract

We show the consistency, relative to a supercompact cardinal, of the least measurable cardinal being both strongly compact and fully Laver indestructible. We also show the consistency, relative to a supercompact cardinal, of the least strongly compact cardinal being somewhat supercompact yet not completely supercompact and having both its strong compactness and degree of supercompactness fully Laver indestructible.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1404 - 1412
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Apter, A., Laver indestructibility and the class of compact cardinals, to appear in this Journal.Google Scholar
[2] Apter, A., On the least strongly compact cardinal, Israel Journal of Mathematics, vol. 35 (1980), pp. 225–233.Google Scholar
[3] Apter, A., On the first n strongly compact cardinals, Proceedings of the American Mathematical Society, vol. 123 (1995), pp. 2229–2235.Google Scholar
[4] Apter, A., Patterns of compact cardinals, Annals of Pure and Applied Logic, vol. 89 (1997), pp. 101–115.CrossRefGoogle Scholar
[5] Cummings, J.. circulated notes.Google Scholar
[6] Gitik, M., A club offormer regulars, to appear in this Journal.Google Scholar
[7] Gitik, M., Changing cofinalities and the nonstationary ideal, Israel Journal of Mathematics, vol. 56 (1986), pp. 280–314.Google Scholar
[8] Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[9] Kimchi, Y. and Magidor, M., The independence between the concepts of compactness and super-compactness, circulated manuscript.Google Scholar
[10] Laver, R., Making the supercompactness of κ indestructible under κ-directed closedforcing, Israel Journal of Mathematics, vol. 29 (1978), pp. 385–388.Google Scholar
[11] Magidor, M., HOW large is the first strongly compact cardinal?, Annals of Mathematical Logic, vol. 10 (1976), pp. 33–57.Google Scholar
[12] Solovay, R., Strongly compact cardinals and the GCH, Tarski symposium, Proceedings of Symposia in Pure Mathematics, no. 25, American Mathematical Society, Providence, 1974, pp. 365–372.Google Scholar