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Let $\mathcal M=(M,<,...)$ be a linearly ordered first-order structure and$T$ its complete theory. We investigate conditions for $T$ that could guaranteethat $\mathcal M$ is not much more complex than some colored orders (linearorders with added unary predicates). Motivated by Rubin's work, we label threeconditions expressing properties of types of $T$ and/or automorphisms of modelsof $T$. We prove several results which indicate the "geometric" simplicity ofdefinable sets in models of theories satisfying these conditions. For example,we prove that the strongest condition characterizes, up to definitionalequivalence (inter-definability), theories of colored orders expanded byequivalence relations with convex classes.

Around Rubin's "Theories of linear order"