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Description

By a result of Simon it is known that a theory of a coloured linear order has quantifier elimination after naming all unary $L$-definable sets and all $L$-definable binary monotone relations. Motivated by this result we define the notion of monotone theories, theories of linear orders in which binary definable sets have previous description. More precisely, an $\aleph_0$-saturated structure $M$ is said to be monotone if there exists an $L$-definable linear order $