  We discuss three problems of Koszmider on the structure of the spaces of
continuous functions on the Stone compact $K_{\mathcal A}$ generated by an
almost disjoint family $\mathcal A$ of infinite subsets of $\omega$ -- we
present a solution to two problems and develop a previous results of
Marciszewski and Pol answering the third one. We will show, in particular, that
assuming Martin's axiom the space $C(K_{\mathcal A})$ is uniquely determined up
to isomorphism by the cardinality of $\mathcal A$ whenever $|{\mathcal
A}|<{\mathfrak c}$, while there are $2^{\mathfrak c}$ nonisomorphic spaces
$C(K_{\mathcal A})$ with $|{\mathcal A}|= {\mathfrak c}$. We also investigate
Koszmider's problems in the context of the class of separable Rosenthal
compacta and indicate the meaning of our results in the language of twisted
sums of $c_0$ and some $C(K)$ spaces.
