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Proof: Part (1) follows form part (2) as the assumption of part (2) follows by
B) > δ (which holds if B = ∅modD), α ∈ B \ (δ + 1) then for every n
S. Shelah (1991)
Reflecting stationary sets and successors of singular cardinalsArchive for Mathematical Logic, 31
Note: as ρ ∈ ω δ, and δ ∈ E clearly β ρ↾ n < δ; so δ ≥ n<ω β ρ↾ n ; as β ρ↾ n ≥ sup range(ρ↾n) contradicting to
M. Gitik (1986)
Changing cofinalities and the nonstationary idealIsrael Journal of Mathematics, 56
Now suppose the second player has a winning strategy in GM * ω+1 (D) which we call
There are Jonsson algebras in many inaccessible cardinals, Ch III Cardinal Arithmetic
Kecheng Liu, S. Shelah (1997)
Cofinalities of elementary substructures of structures on ℵωIsrael Journal of Mathematics, 99
∅ modD has a subset S ′ for which there is a (≤ θ)-square. S ′ = ∅ modD). Then in the game GM * ω+1 (D) (see Definition 8 below), the second player does not have a winning strategy
P. Welch (1989)
MULTIPLE FORCING (Cambridge Tracts in Mathematics 88)Bulletin of The London Mathematical Society, 21
The property on the filter in Definition 1, a kind of large cardinal property, suffices for the proof in Liu Shelah [LiSh484] and is proved consistent as required there (see Conclusion 6). A natural property which looks better, not only is not obtained here, but is shown to be false (in Claim 7). On earlier related theorems see Gitik Shelah [GiSh310]. On such games see e.g. [Je], [Sh-b], [Sh-f].
Archive for Mathematical Logic – Springer Journals
Published: Nov 1, 1996
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