Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-22T13:29:39.401Z Has data issue: false hasContentIssue false
  • English
  • Français

Some structural results concerning supercompact cardinals

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter
Arthur W. Apter*
Affiliation:
Baruch College of CUNY, Department of Mathematics, New York, New York 10010, USA, E-Mail: [email protected], URL: http://math.baruch.cuny.edu/~apter
Get access Rights & Permissions [Opens in a new window]

Abstract.

We show how the forcing of [5] can be iterated so as to get a model containing supercompact cardinals in which every measurable cardinal δ is δ+ supercompact. We then apply this iteration to prove three additional theorems concerning the structure of the class of supercompact cardinals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1919 - 1927
Copyright
Copyright © Association for Symbolic Logic 2001

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., Patterns of compact cardinals, Annals of Pure and Applied Logic, vol. 89 (1997), pp. 101–115.CrossRefGoogle Scholar
[2]Apter, A., Laver indestructibility and the class of compact cardinals, this Journal, vol. 63 (1998), pp. 149–157.Google Scholar
[3]Apter, A., On measurable limits of compact cardinals, this Journal, vol. 64 (1999), pp. 1675–1688.Google Scholar
[4]Apter, A., Supercompactness and measurable limits of strong cardinals, this Journal, vol. 66 (2001), pp. 629–639.Google Scholar
[5]Apter, A. and Shelah, S., “Menas' result is best possible, Transactions of the American Mathematical Society, vol. 349 (1997), pp. 2007–2034.CrossRefGoogle Scholar
[6]Apter, A. and Shelah, S., On the strong equality between supercompactness and strong compactness, Transactions of the American Mathematical Society, vol. 349 (1997), pp. 103–128.CrossRefGoogle Scholar
[7]Burgess, J., Forcing, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 403–452.CrossRefGoogle Scholar
[8]Hamkins, J. D., Gap forcing, Israel Journal of Mathematics, to appear.Google Scholar
[9]Hamkins, J. D., Destruction or preservation as you like it, Annals of Pure and Applied Logic, vol. 91 (1998), pp. 191–229.CrossRefGoogle Scholar
[10]Hamkins, J. D., Gap forcing: Generalizing the Lévy-Solovay theorem, The Bulletin of Symbolic Logic, vol. 5 (1999), pp. 264–272.CrossRefGoogle Scholar
[11]Kimchi, Y. and Magidor, M., The independence between the concepts of compactness and super-compactness, circulated manuscript.Google Scholar
[12]Lévy, A. and Solovay, R., Measurable cardinals and the continuum hypothesis, Israel Journal of Mathematics, vol. 5 (1967), pp. 234–248.CrossRefGoogle Scholar
[13]Magidor, M., How large is the first strongly compact cardinal?, Annals of Mathematical Logic, vol. 10 (1976), pp. 33–57.CrossRefGoogle Scholar
[14]Mekler, A. and Shelah, S., Does κ-free imply strongly κ-free?, Proceedings of the Third Conference on Abelian Group Theory (Salzburg), Gordon and Breach, 1987, pp. 137–148.Google Scholar
[15]Menas, T., On strong compactness and supercompactness, Annals of Mathematical Logic, vol. 7 (1974), pp. 327–359.CrossRefGoogle Scholar