Schimmerling asked whether □λ∗+GCH$\square ^{\ast }_{\lambda }+\mathsf {GCH}$ entails the existence of a λ+-Souslin tree, for a singular cardinal λ. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E≠cf(λ)λ+${E}^{{\lambda }^{+}}_{{\neq } \text {cf}(\lambda )}$. As a bonus, the outcome λ+-Souslin tree is moreover free.

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对席默林问题的评论

Schimmerling 询问 □λ∗+GCH$\square ^{\ast }_{\lambda }+\mathsf {GCH}$ 是否需要存在 λ+-Souslin 树，对于奇异基数 λ。我们在额外假设下提供了肯定的答案，即存在 E≠cf(λ)λ+${E}^{{\lambda }^{+}}_{{\neq } \text 的非反射平稳子集{cf}(\lambda )}$。作为奖励，结果 λ+-Souslin 树也是免费的。