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Splitting P κλ into stationary subsets

Published online by Cambridge University Press:  12 March 2014

Yo Matsubara
Yo Matsubara*
Affiliation:
Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
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Abstract

We show that if κ is an inaccessible cardinal then P κλ splits into λ<κ many disjoint stationary subsets. We also show that if P κλ carries a strongly saturated ideal then the nonstationary ideal cannot be λ+-saturated.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 2 , June 1988 , pp. 385 - 389
Copyright
Copyright © Association for Symbolic Logic 1988

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References

REFERENCES

[1] Baumgartner, J. E. and Taylor, A. D., Saturation properties of ideals in generic extensions. I, Transactions of the American Mathematical Society, vol. 270 (1982), pp. 557–573.CrossRefGoogle Scholar
[2] Baumgartner, J. E., Taylor, A. D., and Wagon, S., On splitting stationary subsets of large cardinals, this Journal, vol. 42 (1977), pp. 203–214.Google Scholar
[3] Carr, D. M., The minimal normal filter on P κλ, Proceedings of the American Mathematical Society, vol. 86 (1982), pp. 316–320.Google Scholar
[4] Foreman, M., Potent axioms, Transactions of the American Mathematical Society, vol. 294(1986), pp. 1–28.CrossRefGoogle Scholar
[5] Foreman, M., Notes from set theory seminar U.C.L.A., 1981/82.Google Scholar
[6] Gitik, M., Nonsplitting subset of (κ+), this Journal, vol. 50 (1985), pp. 881–894.Google Scholar
[7] Jech, T. J., Some combinatorial problems concerning uncountable cardinals, Annals of Mathematical Logic, vol. 5 (1973), pp. 165–198.Google Scholar
[8] Jech, T. J. and Prikry, K., Ideals over uncountable sets: Applications of almost disjoint functions and generic ultrapowers , Memoirs of the American Mathematical Society, no. 214 (1979).Google Scholar
[9] Magidor, M., Representing sets of ordinals as countable unions of sets in the core model (to appear).Google Scholar
[10] Matsubara, Y., Menas' conjecture and generic ultrapowers, Annals of Pure and Applied Logic, vol. 36(1987), pp. 225–234.Google Scholar
[11] Matsubara, Y., Filters related to supercompact cardinals, Ph.D. thesis, UCLA, Los Angeles, California, 1985.Google Scholar
[12] Menas, T. K., On strong compactness and supercompactness, Annals of Mathematical Logic, vol. 7 (1975), pp. 327–359.CrossRefGoogle Scholar
[13] Namba, K., On the closed unbounded ideal of ordinal numbers, Commentarii Mathematici Universitatis Sancti Pauli, vol. 22 (1974), pp. 33–56.Google Scholar
[14] Zwicker, W. S., Partial results on splitting stationary subsets of P κλ (unpublished).Google Scholar