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Preserving σ-ideals

Published online by Cambridge University Press:  12 March 2014

Jindřich Zapletal
Jindřich Zapletal*
Affiliation:
Division of Mathematics and Astronomy, California Institute of Technology, Pasadena. CA 91125, USA. E-mail: [email protected]
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Abstract

It is proved consistent that there be a proper σ-ideal on ω1 and an ℵ1-preserving poset ℙ such that ℙ ⊩ the σ-ideal generated by is not proper.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1437 - 1441
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Baumgartner, J. E., Applications of the proper forcing axiom, Handbook of set-theoretical topology (Kunen, K. and Vaughan, J. E., editors), North-Holland, Amsterdam, 1984, pp. 913–959.CrossRefGoogle Scholar
[2] Baumgartner, J. E. and Taylor, A. D., Saturation properties of ideals in generic extensions II, Transactions of the American Mathematical Society, vol. 271 (1982), pp. 587–609.Google Scholar
[3] Foreman, M., Magidor, M., and Shelah, S., Martin's maximum saturated ideals and nonregular filters I, Annals of Mathematics, vol. 127 (1988), pp. 1–47.Google Scholar
[4] Jech, T. J., Set theory, Academic Press, New York, 1978.Google Scholar
[5] Namba, K., Independence proof of (ω, ω α) distributive law in complete Boolean algebras, Commentarii Mathematici Universitatis Sancti Pauli, vol. 19 (1970), pp. 1–12.Google Scholar
[6] Shelah, S., Proper forcing, Springer-Verlag, New York, 1982.CrossRefGoogle Scholar
[7] Woodin, W. H., The continnum hypothesis, the axiom of determinacy and the nonstationary ideal, to appear.Google Scholar