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Cardinal preserving ideals

Published online by Cambridge University Press:  12 March 2014

Moti Gitik  and
Saharon Shelah
Moti Gitik
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
Saharon Shelah
Affiliation:
Department of Mathematics, Hebrew University of Jerusalem, Jerusalem. Israel, E-mail: shelah@math.huji.ac.il
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Abstract

We give some general criteria, when κ-complete forcing preserves largeness properties—like κ-presaturation of normal ideals on λ (even when they concentrate on small cofinalities). Then we quite accurately obtain the consistency strength “NSλ is αi-preserving”, for λ > α2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1527 - 1551
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Avraham, U., Isomorphism of Aronszajn trees, Ph.D. thesis, Jerusalem, 1979.Google Scholar
[2]Baumgartner, J., Independence results in set theory, Notices of the American Mathematical Society, vol. 25 (1978), pp. A 248–249.Google Scholar
[3]Baumgartner, J. and Taylor, A., Ideals in generic extensions, II, Transactions of the American Mathematical Society, vol. 271 (1982), pp. 587–609.Google Scholar
[4]Galvin, F., Jech, T., and Magidor, M., An ideal game, this Journal, vol. 43 (1978), pp. 284–292.Google Scholar
[5]Gitik, M., The nonstationary ideal on α2, Israel Journal of Mathematics, vol. 48 (1984), pp. 257–288.CrossRefGoogle Scholar
[6]Gitik, M., Changing cofinalities and the nonstationary ideal, Israel Journal of Mathematics, vol. 56 (1986), pp. 280–314.CrossRefGoogle Scholar
[7]Gitik, M., ¬SCH from O(κ) = κ++, Annals of Pure and Applied Logic, vol. 43 (1989), pp. 209–234.CrossRefGoogle Scholar
[8]Gitik, M., On generic elementary embeddings, this Journal, vol. 54 (1989), no. 3, pp. 700–707.Google Scholar
[9]Gitik, M., Some results on the nonstationary ideal, Israel Journal of Mathematics, vol. 92 (1995), pp. 61–112.CrossRefGoogle Scholar
[10]Gitik, M., Some results on the nonstationary ideal II, Israel Journal of Mathematics, vol. 99 (1997), pp. 175–188.CrossRefGoogle Scholar
[11]Gitik, M., On clubs consisting of former regulars, this Journal, vol. 64 (1999), pp. 1–12.Google Scholar
[12]Harrington, L. and Shelah, S., Equiconsistency results in set theory, Notre Dame Journal of Formal Logic, vol. 26 (1985), no. 2, pp. 178–188.CrossRefGoogle Scholar
[13]Jech, T., Magidor, M., Mitchell, W., and Prikry, K., Precipitous ideals, this Journal, vol. 45 (1980), pp. 1–8.Google Scholar
[14]Mitchell, W., The core model for sequence of measures II, preprint.Google Scholar
[15]Mitchell, W., The core model for sequences of measures I, Mathematical Proceedings of the Cambridge Philisophical Society, vol. 95 (1984), pp. 229–260.CrossRefGoogle Scholar
[16]Mitchell, W., Indiscernibles, skies and ideals, Contemporary Mathematics, vol. 31 (1984), pp. 161–182.CrossRefGoogle Scholar
[17]Shelah, S., Proper forcing, Lecture Notes in Mathematics, no. 940, Springer-Verlag, 1982.CrossRefGoogle Scholar
[18]Shelah, S., Some notes on iterated forcing with 2α0 > α2, Notre Dame Journal of Formal Logic, vol. 29 (1988), pp. 1–17.Google Scholar