论文标题
部分可观测时空混沌系统的无模型预测
Sharp Vaught's Conjecture for Some Classes of Partial Orders
论文作者
论文摘要
Matatyahu Rubin表明，Vaught的猜想的鲜明版本，$ i（{\ Mathcal t}，ω）\ in \ {0,1，{\ Mathfrak {\ Mathfrak {c}}} \} $，用于线性顺序$ {\ Mathcal t} $的每个完整理论。我们表明，对于每个完整的部分秩序理论，在包含线性订单类别的最小部分顺序中具有模型，并且在有限产物和有限的脱节工会下关闭。对于以相同方式获得的有限的单态分解，植根树的延伸也同样。 Vaught的猜想的敏锐版本也适用于树木的理论，这些理论是线性订单的无连接工会。
Matatyahu Rubin has shown that a sharp version of Vaught's conjecture, $I({\mathcal T},ω)\in \{ 0,1,{\mathfrak{c}}\}$, holds for each complete theory of linear order ${\mathcal T}$. We show that the same is true for each complete theory of partial order having a model in the the minimal class of partial orders containing the class of linear orders and which is closed under finite products and finite disjoint unions. The same holds for the extension of the class of rooted trees admitting a finite monomorphic decomposition, obtained in the same way. The sharp version of Vaught's conjecture also holds for the theories of trees which are infinite disjoint unions of linear orders.
