Notre Dame Journal of Formal Logic

A Tail Club Guessing Ideal Can Be Saturated without Being a Restriction of the Nonstationary Ideal

Tetsuya Ishiu

Abstract

We outline the proof of the consistency that there exists a saturated tail club guessing ideal on ω₁ which is not a restriction of the nonstationary ideal. A new class of forcing notions and the forcing axiom for the class are introduced for this purpose.

Article information

Source
Notre Dame J. Formal Logic, Volume 46, Number 3 (2005), 327-333.

Dates
First available in Project Euclid: 30 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1125409331

Digital Object Identifier
doi:10.1305/ndjfl/1125409331

Mathematical Reviews number (MathSciNet)
MR2162103

Zentralblatt MATH identifier
1095.03040

Subjects
Primary: 03E35: Consistency and independence results
Secondary: 03E55: Large cardinals

Keywords
club guessing saturated forcing axiom

Citation

Ishiu, Tetsuya. A Tail Club Guessing Ideal Can Be Saturated without Being a Restriction of the Nonstationary Ideal. Notre Dame J. Formal Logic 46 (2005), no. 3, 327--333. doi:10.1305/ndjfl/1125409331. https://projecteuclid.org/euclid.ndjfl/1125409331


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References

  • [1] Baumgartner, J. E., A. D. Taylor, and S. Wagon, "On splitting stationary subsets of large cardinals", The Journal of Symbolic Logic, vol. 42 (1977), pp. 203--14.
  • [2] Džamonja, M., and S. Shelah, "On squares, outside guessing of clubs and $I\sb <f[\lambda]$", Fundamenta Mathematicae, vol. 148 (1995), pp. 165--98.
  • [3] Foreman, M., M. Magidor, and S. Shelah, "Martin's maximum, saturated ideals, and nonregular ultrafilters", Annals of Mathematics. Second Series, vol. 129 (1989), p. 651.
  • [4] Foreman, M., and P. Komjáth, "The club guessing ideal (commentary on a theorem of Gitik and Shelah)", forthcoming in the Journal of Mathematical Logic.
  • [5] Goldring, N., "Woodin cardinals and presaturated ideals", Annals of Pure and Applied Logic, vol. 55 (1992), pp. 285--303.
  • [6] Ishiu, T., "Club guessing sequences and filters", forthcoming in the The Journal of Symbolic Logic.
  • [7] Ishiu, T., "The saturation of club guessing ideal", preprint, 2005.
  • [8] Kojman, M., and S. Shelah, "The universality spectrum of stable unsuperstable theories", Annals of Pure and Applied Logic, vol. 58 (1992), pp. 57--72.
  • [9] Shelah, S., Cardinal arithmetic, vol. 29 of Oxford Logic Guides, The Clarendon Press, New York, 1994.
  • [10] Shelah, S., Proper and Improper Forcing, 2d edition, Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1998.
  • [11] Woodin, W. H., The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, vol. 1 of De Gruyter Series in Logic and Its Applications, Walter de Gruyter & Co., Berlin, 1999.