  We prove that if continuum is not a Kunen cardinal, then there is a uniform
Eberlein compact space $K$ such that the Banach space $C(K)$ does not embed
isometrically into $\ell_\infty/c_0$. We prove a similar result for isomorphic
embeddings. We also construct a consistent example of a uniform Eberlein
compactum whose space of continuous functions embeds isomorphically into
$\ell_\infty/c_0$, but fails to embed isometrically. As far as we know it is
the first example of this kind.
