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Saturation of the weakly compact ideal
Author(s):
Alex
Hellsten
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3323-3334.
MSC (2010):
Primary 03E55, 03E35
Posted:
May 17, 2010
MathSciNet review:
2653962
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Additional information
Abstract:
It is consistent relative to a measurable cardinal of order that the ideal associated with a weakly compact cardinal of order is saturated.
References:
-
- 1.
- James E. Baumgartner, Iterated forcing, Surveys in Set Theory (A. R. D. Mathias, ed.), London Math. Soc. Lecture Note Ser., vol. 87, Cambridge University Press, 1983, pp. 1-59. MR 823775 (87c:03099)
- 2.
- 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 0505505 (58:21619)
- 3.
- Moti Gitik and Saharon Shelah, Less saturated ideals, Proc. Amer. Math. Soc. 125 (1997), 1523-1530. MR 1363421 (97g:03055)
- 4.
- Alex Hellsten, Diamonds on large cardinals, Ann. Acad. Sci. Fenn. Math. Diss. 134 (2003). MR 2026390 (2004j:03054)
- 5.
- -, Orders of indescribable sets, Arch. Math. Logic 45 (2006), no. 6, 705-714. MR 2252250 (2007d:03092)
- 6.
- Thomas 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 (87d:03139)
- 7.
- Wenzhi Sun, Stationary cardinals, Arch. Math. Logic 32 (1993), no. 6, 429-442. MR 1245524 (94i:03103)
- 8.
- Alfred Tarski, Ideale in vollständigen Mengenkörpern. II, Fund. Math. 33 (1945), 51-65. MR 0017737 (8:193b)
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Additional Information:
Alex
Hellsten
Affiliation:
Finnish Matriculation Examination Board, P.O. Box 50, 00581 Helsinki, Finland
Email:
alex.hellsten@iki.fi
DOI:
10.1090/S0002-9939-2010-10399-4
PII:
S 0002-9939(2010)10399-4
Received by editor(s):
October 27, 2006
Received by editor(s) in revised form:
January 21, 2010
Posted:
May 17, 2010
Communicated by:
Julia Knight
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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