as the title says I am asked to prove the following:
Let $T=\{c_m\neq c_n: m,n\in \mathbb{N}, m\neq n \}$ in the language $L=\{c_n : n\in \mathbb{N}\}$, where each $c_n$ is a constant symbol. Prove that T is not $\aleph_0$-categorical. Prove also that $T$ is $\mathcal{k}$-categorical for each cardinal $\mathcal{k}>\aleph_0$.
I thought a lot about this but I can't manage to prove it. Any help is appreciated :)