Let ${\sf DLO}$ be the theory of dense linear orders without endpoints. Let $c_i$, for $i \in \mathbb N$, be new constant symbols, and let ${\sf DLO}'={\sf DLO}\cup \{ c_i < c_{i+1} \mid i \in \mathbb N\}$. We know that ${\sf DLO}'$ is a complete theory, and has exactly three countable models up to isomorphisms. Deduce which among the three are atomic, and which among the three are saturated.
We have covered in lectures that any prime models in a countable language are countable and atomic. However, how could this be used, if at all? I also am struggling to grasp the intuitive understanding of saturated models; what are some well known and easy enough models that are saturated, or in general, $\kappa$-saturated for some infinite or fitie $\kappa$?