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Nonsplitting subset of κ(κ+)

Published online by Cambridge University Press:  12 March 2014

Moti Gitik
Moti Gitik*
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
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Abstract

Assuming the existence of a supercompact cardinal, we construct a model of ZFC + (There exists a nonsplitting stationary subset of ). Answering a question of Uri Abraham [A], [A-S], we prove that adding a real to the world always makes stationary

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 50 , Issue 4 , December 1985 , pp. 881 - 894
Copyright
Copyright © Association for Symbolic Logic 1985

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References

REFERENCES

[A]Abraham, U., Isomorphism of Aronszajn trees, Ph.D. Thesis, Jerusalem, 1979.Google Scholar
[A-S]Abraham, U. and Shelah, S., Forcing closed unbounded sets, this Journal, vol. 48 (1983), pp. 643–657.Google Scholar
[B-H-K]Baumgartner, J., Harrington, L. and Kleinberg, E., Adding a closed unbounded set, this Journal, vol. 41 (1976), pp. 481–482.Google Scholar
[J1]Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[J2]Jech, T., Some combinatorial problems concerning uncountable cardinals, Annals of Mathematical Logic, vol. 5 (1973), pp. 165–198.CrossRefGoogle Scholar
[K]Kueker, D., Löwenheim-Skolem and interpolation theorems in infinitary languages, Bulletin of the American Mathematical Society, vol. 78 (1972), pp. 211–215.CrossRefGoogle Scholar
[Ma1]Magidor, M., How large is the first strongly compact cardinal? Annals of Mathematical Logic, vol. 10 (1976), pp. 33–57.CrossRefGoogle Scholar
[Ma2]Magidor, M., On the covering lemma, Lecture presented at the American Mathematical Society Summer Research Conference on Axiomatic Set Theory, Boulder, Colorado, 1983 (not published).Google Scholar
[Me]Menas, T. K., On strong compactness and supercompactness, Annals of Mathematical Logic, vol. 7 (1974), pp. 327–359.CrossRefGoogle Scholar
[R]Radin, L., Adding closed cofinal sequences to large cardinals, Annals of Mathematical Logic, vol. 23 (1982), pp. 263–283.Google Scholar
[Sh]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[S]Solovay, R., Real-valued measurable cardinals, Axiomatic set theory (Scott, D. S., editor), Proceedings of Symposia in Pure Mathematics, vol. 13, part 1, American Mathematical Society, Providence, Rhode Island, 1971, pp. 397–428.CrossRefGoogle Scholar
[W]Woodin, H., Saturated ideals over the first inaccessible (in preparation).Google Scholar
[Z]Zwicker, W., Partial results on splitting stationary subsets of (to appear).Google Scholar