Let $\mathcal M=(M,<,\ldots)$ be a linearly ordered first-order structure and T its complete theory. We investigate conditions for T that could guarantee that $\mathcal M$ is not much more complex than some colored orders (linear orders with added unary predicates). Motivated by Rubin’s work [5], we label three conditions expressing properties of types of T and/or automorphisms of models of T. We prove several results which indicate the “geometric” simplicity of definable sets in models of theories satisfying these conditions. For example, we prove that the strongest condition characterizes, up to definitional equivalence (inter-definability), theories of colored orders expanded by equivalence relations with convex classes.

中文翻译：

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围绕鲁宾的“线性秩序理论”

让$\mathcal M=(M,<,\ldots)$是一个线性有序的一阶结构和吨其完整的理论。我们调查条件吨这可以保证$\数学 M$并不比一些彩色订单（添加一元谓词的线性订单）复杂多少。受 Rubin 的工作 [5] 的启发，我们标记了三个条件来表示类型的属性吨和/或模型的自同构吨. 我们证明了几个结果，这些结果表明满足这些条件的理论模型中可定义集合的“几何”简单性。例如，我们证明了最强条件表征了定义等价（inter-definability），通过与凸类的等价关系扩展的彩色顺序理论。