  We indicate a way of distinguishing between structures, for which, two
structures are said to be separable.Being separable implies being
non-isomorphic. We show that for any first order theory $T$ in a countable
language, if it has an uncountable set of countable models that are pairwise
separable, then actually it has such a set of size $2^{\aleph_0}$. Our result
follows trivially assuming the Continuum Hypothesis ($CH$). We work here in
$ZFC$ (only without $CH$).
