We show that the poset of copies ℙ ( ℚ n ) = 〈 { f [ X ] : f ∈ Emb ( ℚ n ) } , ⊂ 〉 $\mathbb {P} (\mathbb {Q}_{n} )=\langle \{ f[X]: f\in \text {Emb} (\mathbb {Q}_{n} ) \},\subset \rangle $ of the countable homogeneous universal n -labeled linear order, ℚ n $\mathbb {Q}_{n}$ , is forcing equivalent to the poset S ∗ π $\mathbb {S} \ast \pi $ , where S $\mathbb {S}$ is the Sacks perfect set forcing and 1 S ⊢ “π $1_{\mathbb {S}} \Vdash `` \pi $ is an atomless separative σ -closed forcing”. Under CH (or under some weaker assumptions) 1 S ⊢ “π $1_{\mathbb {S}} \Vdash `` \pi $ is forcing equivalent to P ( ω )/Fin”. In addition, these statements hold for each countable non-scattered n -labeled linear order L $\mathbb {L}$ and we have rosq ℙ ( L ) ≅ rosq ℙ ( ℚ n ) ≅ rosq ( S ∗ π ) $\text {ro} \text {sq} \mathbb {P} (\mathbb {L} )\cong \text {ro} \text {sq} \mathbb {P} (\mathbb {Q}_{n} )\cong \text {ro} \text {sq} (\mathbb {S} \ast \pi )$ .

中文翻译：

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可数非分散标记线性阶数的副本集

我们证明了副本的偏序集 ℙ ( ℚ n ) = 〈 { f [ X ] : f ∈ Emb ( ℚ n ) } , ⊂ 〉 $\mathbb {P} (\mathbb {Q}_{n} )=\ langle \{ f[X]: f\in \text {Emb} (\mathbb {Q}_{n} ) \},\subset \rangle $ 可数齐次通用 n 标记线性阶数，ℚ n $\ mathbb {Q}_{n}$ ，是强制等价于偏序 S ∗ π $\mathbb {S} \ast \pi $ ，其中 S $\mathbb {S}$ 是 Sacks 完美集合强制和 1 S ⊢ “π $1_{\mathbb {S}} \Vdash `` \pi $ 是一个无原子分离的 σ 闭合强迫”。在 CH（或在一些较弱的假设下） 1 S ⊢ “π $1_{\mathbb {S}} \Vdash `` \pi $ 强制等效于 P ( ω )/Fin”。此外，