Countable, 1-transitive, coloured linear orderings I

We give a classification of all the countable, 1-transitive, coloured linear orderings for countable colour sets. This is a generalization of Morelʹs classification of the countable, 1-transitive linear orderings. For finite colour sets, there are ℵ1 examples and for countably infinite colour sets, there are 2ℵ0 (discussed in more detail in a subsequent paper (countable, 1-transitive, coloured linear orderings II, submitted)). We also include a classification of the countable homogeneous coloured linear orders.