I'm stuck in this problem where i have a language $L$ with signature being a one equivalence relationship $R$, and a theory over this relation with infinite many infinite equivalence classes.
I need to know how many models of cardinality $\aleph_0$ are ther for this Theory, everyone around seem to find trivial to claim that there is just one model with this characteristics, but i don't get how to prove this. I've been trying to build an isomorphism between two arbitrary countable models $\mathfrak{A}$, $\mathfrak{B}$. Making $h(a) = b$ for some $a$ $\in A$ and $b \in B$ But i don't know how to keep going.