AI 中文总结
研究在连续统假设下添加$\square_{\aleph_1}$的力迫概念$\mathbb P$，证明其可实现为$\aleph_2$-苏斯林树，更一般地，$\square_\lambda$可由$\lambda^+$-苏斯林树添加，构造统一且可扩展到不可达基数。
AI 中文摘要
福尔曼和马吉多尔表明连续统假设意味着存在一个可数封闭的$\aleph_2$-链条件力迫概念$\mathbb P$用于添加$\square_{\aleph_1}$。在此，我们表明$\mathbb P$可一致地实现为一个$\aleph_2$-苏斯林树。更一般地，我们证明$\square_\lambda$可由一个$\lambda^+$-苏斯林树添加，这是在奇异基数后继层面上福尔曼 - 马吉多尔力迫的首个类似物。我们的构造是统一的且可扩展到不可达基数。
英文摘要
Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed $\aleph_2$-cc forcing notion $\mathbb P$ for adding $\square_{\aleph_1}$. Here, we show that $\mathbb P$ may consistently be realized as an $\aleph_2$-Souslin tree. More generally, we prove that $\square_λ$ may be added by a $λ^+$-Souslin tree, providing the first analog of the Foreman--Magidor forcing at the level of successors of singular cardinals. Our construction is uniform and extends to inaccessible cardinals as well.
