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Nonreflecting stationary subsets of $P_κλ$

100%

Abe Y.

Fundamenta Mathematicae

2000

tom 165

nr 1

55-66

We explore the possibility of forcing nonreflecting stationary sets of $P_κλ$. We also present a $P_κλ$ generalization of Kanamori's weakly normal filters, which induces stationary reflection.

Weakly normal ideals ou PKl and the singular cardinal hypothesis

100%

Abe Y.

Fundamenta Mathematicae

1993

tom 143

nr 2

97-106

In §1, we observe that a weakly normal ideal has a saturation property; we also show that the existence of certain precipitous ideals is sufficient for the existence of weakly normal ideals. In §2, generalizing Solovay's theorem concerning strongly compact cardinals, we show that $λ^{<κ}$ is decided if $P_κλ$ carries a weakly normal ideal and λ is regular or cf λ ≤ κ. This is applied to solving the singular cardinal hypothesis.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Abe Y.

1 2000

1 1993

Wyniki wyszukiwania

Nonreflecting stationary subsets of $P_κλ$

Weakly normal ideals ou PKl and the singular cardinal hypothesis