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In the paper below Rosenstein gives a complete characterization of $\aleph_0$-categorcial theories of linear order.

Rosenstein, Joseph G. $\aleph _{0}$ℵ0-categoricity 0$-categoricity of linear orderings. Fund. Math. 64 1969 1–5.

You can also find the result, and many other gems, in Rosenstein majestic text on linear orders.

show/hide this revision's text 1

In the paper below Rosenstein gives a complete characterization of $\aleph_0$-categorcial theories of linear order.

Rosenstein, Joseph G. $\aleph _{0}$ℵ0-categoricity of linear orderings. Fund. Math. 64 1969 1–5.

You can also find the result, and many other gems, in Rosenstein majestic text on linear orders.