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A variant of the diamond principle
for combinatorial ideals


Author: Y. Abe
Journal: Proc. Amer. Math. Soc. 127 (1999), 847-849
MSC (1991): Primary 03E05, 03E55
DOI: https://doi.org/10.1090/S0002-9939-99-04528-1
MathSciNet review: 1468178
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Abstract: We use a variant of the diamond principle to show many ideals on $\kappa$ are not $2^{\kappa}$-saturated if $\kappa$ is large. For instance, the $\Pi^1_1$-indescribable ideal is not $2^{\kappa}$-saturated if $\kappa$ is almost ineffable.


References [Enhancements On Off] (What's this?)

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  • 2. J. Baumgartner, A. Taylor and S. Wagon, On splitting stationary subsets of large cardinals, J. Symbolic Logic 42 (1977), 203-214. MR 58:21619
  • 3. C. A. Johnson, Distributive ideals and partition relations, J. Symbolic Logic 51 (1986), 617-625. MR 87j:03076
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Additional Information

Y. Abe
Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221, Japan
Email: yabe@cc.kanagawa-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-99-04528-1
Keywords: The diamond principle, saturated ideals, ineffability, indescribability
Received by editor(s): October 9, 1996
Received by editor(s) in revised form: June 5, 1997
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1999 American Mathematical Society

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