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A variant of the diamond principle for combinatorial ideals

Author(s): Y. Abe
Journal: Proc. Amer. Math. Soc. 127 (1999), 847-849.
MSC (1991): Primary 03E05, 03E55
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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:

1.: J. Baumgartner, Ineffability properties of cardinals 1, Infinite and finite sets (P. Erdös 60th Birthday Colloquium, Keszthely, Hungary, 1973), Colloquia Mathematica Societatis János Bolyai, vol. 10, North-Holland, Amsterdam (1975), 109-130. MR 52:5427
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
4.: C. A. Johnson, More on distributive ideals, Fund. Math. 128 (1987), 113-130. MR 89a:03095


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