Saturation of the weakly compact ideal

Hellsten, Alex

doi:10.1090/S0002-9939-2010-10399-4

Saturation of the weakly compact ideal

Author: Alex Hellsten
Journal: Proc. Amer. Math. Soc. 138 (2010), 3323-3334
MSC (2010): Primary 03E55, 03E35
DOI: https://doi.org/10.1090/S0002-9939-2010-10399-4
Published electronically: May 17, 2010
MathSciNet review: 2653962
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is consistent relative to a measurable cardinal of order $\alpha$ that the ideal associated with a weakly compact cardinal of order $\alpha$ is saturated.

References

James E. Baumgartner, Iterated forcing, Surveys in set theory, London Math. Soc. Lecture Note Ser., vol. 87, Cambridge Univ. Press, Cambridge, 1983, pp. 1–59. MR 823775, DOI https://doi.org/10.1017/CBO9780511758867.002
James E. Baumgartner, Alan D. Taylor, and Stanley Wagon, On splitting stationary subsets of large cardinals, J. Symbolic Logic 42 (1977), no. 2, 203–214. MR 505505, DOI https://doi.org/10.2307/2272121
Moti Gitik and Saharon Shelah, Less saturated ideals, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1523–1530. MR 1363421, DOI https://doi.org/10.1090/S0002-9939-97-03702-7
Alex Hellsten, Diamonds on large cardinals, Ann. Acad. Sci. Fenn. Math. Diss. 134 (2003), 48. Dissertation, University of Helsinki, Helsinki, 2003. MR 2026390
Alex Hellsten, Orders of indescribable sets, Arch. Math. Logic 45 (2006), no. 6, 705–714. MR 2252250, DOI https://doi.org/10.1007/s00153-006-0015-1
Thomas J. Jech and W. Hugh Woodin, Saturation of the closed unbounded filter on the set of regular cardinals, Trans. Amer. Math. Soc. 292 (1985), no. 1, 345–356. MR 805967, DOI https://doi.org/10.1090/S0002-9947-1985-0805967-1
Wen Zhi Sun, Stationary cardinals, Arch. Math. Logic 32 (1993), no. 6, 429–442. MR 1245524, DOI https://doi.org/10.1007/BF01270466
Alfred Tarski, Ideale in vollständigen Mengenkörpern. II, Fund. Math. 33 (1945), 51–65 (German). MR 17737, DOI https://doi.org/10.4064/fm-33-1-51-65