论文标题
非线性迭代和更高的分裂
Non-linear iterations and higher splitting
论文作者
论文摘要
我们表明，在不可访问的红衣主教$κ$上，最终狭窄的序列被保留在Cummings-shaleh的非线性迭代中，高于$κ$。此外，假设GCH，$κ^{<κ} =κ$，我们表明： （1）如果$κ$可以强烈展开，则$κ^+\leqβ= \ hbox {cf}（β）\ leq \ hbox {cf}（δ）\leqΔ\ leqleqμ$和$ \ hbox {cf}（cf}（cf}（cf}（cf）） $ \ mathfrak {s}（κ）=κ^+\ leq \ mathfrak {b}（κ）=β\ leq \ leq \ mathfrak {d}（κ）=Δ\ leq 2^κ=μ。$ $ $ $ $κ$，如果$κ$ incccessiens inccessiens inccessiens inccessiens inccessiens inccessiens inccessient inccessient $ <κ$ - 支持的$κ$ -HECHLER强迫$λ$的$κ$ - $κ$ - 长度的$λ$。
We show that generalized eventually narrow sequences on a strongly inaccessible cardinal $κ$ are preserved under the Cummings-Shaleh non-linear iterations of the higher Hechler forcing on $κ$. Moreover assuming GCH, $κ^{<κ}=κ$, we show that: (1) if $κ$ is strongly unfoldable, $κ^+\leqβ=\hbox{cf}(β)\leq \hbox{cf}(δ)\leqδ\leqμ$ and $\hbox{cf}(μ)>κ$,then there is a cardinal preserving generic extension in which $$\mathfrak{s}(κ)=κ^+\leq\mathfrak{b}(κ)=β\leq\mathfrak{d}(κ)=δ\leq 2^κ=μ.$$ (2) if $κ$ is strongly inaccessible, $λ>κ^+$, then in the generic extension obtained as the $<κ$-support iteration of $κ$-Hechler forcing of length $λ$ there are no $κ$-towers of length $λ$.
