Sailing over three problems of Koszmider

We discuss three problems of Koszmider on the structure of the spaces of continuous functions on the Stone compact K_A generated by an almost disjoint family A of infinite subsets of ω— 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_A) is uniquely determined up to isomorphism by the cardinality of A whenever|A|<c, while there are 2^c nonisomorphic spaces C(K_A) with|A|=c. We also investigate Koszmider’s problems in the context of the class of separable Rosenthal compacta and indicate the meaningof our results in the language of twisted sums of c₀ and some C(K) spaces.