Journal of Symbolic Logic

Fat sets and saturated ideals

John Krueger

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Abstract

We strengthen a theorem of Gitik and Shelah [GS] by showing that if κ is either weakly inaccessible or the successor of a singular cardinal and S is a stationary subset of κ such that NSκS is saturated then κ ∖ S is fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [BT], showing in particular that if I is a λ+++-saturated normal ideal on Pκ λ then the conditions of being λ+-preserving, weakly presaturated, and presaturated are equivalent for I.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 3 (2003), 837- 845.

Dates
First available in Project Euclid: 17 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1058448442

Digital Object Identifier
doi:10.2178/jsl/1058448442

Mathematical Reviews number (MathSciNet)
MR2004h:03097

Zentralblatt MATH identifier
1056.03024

Citation

Krueger, John. Fat sets and saturated ideals. J. Symbolic Logic 68 (2003), no. 3, 837-- 845. doi:10.2178/jsl/1058448442. https://projecteuclid.org/euclid.jsl/1058448442


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References

  • U. Abraham and S. Shelah Forcing closed unbounded sets, Journal of Symbolic Logic, vol. 48 (1983), no. 3, pp. 643--657.
  • J. Baumgartner and A. Taylor Saturation properties of ideals in generic extensions II, Transactions of the American Mathematical Society, vol. 271 (1982), no. 2, pp. 587--609.
  • D. Burke and Y. Matsubara The extent of strength in the club filters, Israel Journal of Mathematics, vol. 114 (1999), pp. 253--263.
  • J. Cummings Collapsing successors of singulars, Proceedings of the American Mathematical Society, vol. 125 (1997), no. 9, pp. 2703--2709.
  • M. Foreman, M. Magidor, and S. Shelah Martin's maximum, saturated ideals, and non-regular ultrafilters. Part I, Annals of Mathematics, vol. 127 (1988), no. 3, pp. 1--47.
  • M. Gitik and S. Shelah Less saturated ideals, Proceedings of the American Mathematical Society, vol. 125 (1997), no. 5, pp. 1523--1530.
  • T. Jech Set theory, Springer-Verlag,1997.
  • M. Magidor Reflecting stationary sets, Journal of Symbolic Logic, vol. 47 (1982), no. 4, pp. 755--771.
  • S. Shelah Cardinal arithmetic, Oxford University Press,1994.