论文标题
继任枢机主教的紧凑与崇拜
Compactness versus hugeness at successor cardinals
论文作者
论文摘要
如果$κ$是常规的，$ 2^{<κ} \leqκ^+$，则在$κ^+$上存在弱国有的理想，意味着$ \ square^*_κ$。这部分回答了工头和马格多尔关于$ω_2$上可接近理想的问题。作为推论，我们表明，如果在$ω_2$上有一个预饱和的理想$ i $，以便$ \ mathcal {p}（ω_2）/i $是semipoper，则CH持有。我们还展示了在传统强迫方法中同时在继任的基数上同时获得树木特性和饱和理想的障碍。
If $κ$ is regular and $2^{<κ}\leqκ^+$, then the existence of a weakly presaturated ideal on $κ^+$ implies $\square^*_κ$. This partially answers a question of Foreman and Magidor about the approachability ideal on $ω_2$. As a corollary, we show that if there is a presaturated ideal $I$ on $ω_2$ such that $\mathcal{P}(ω_2)/I$ is semiproper, then CH holds. We also show some barriers to getting the tree property and a saturated ideal simultaneously on a successor cardinal from conventional forcing methods.
