The Ramsey property for Cp(X)

For a Tychonoff space X, we denote by C-p(X) the space of real-valued continuous functions with the topology of pointwise convergence. We show that (a) Arhangel'skii's property (alpha(2)) and the Ramsey property introduced by Nogura and Shakhmatov are equivalent for C-p(X), (b) the Ramsey property and Nyikos' property (alpha(3/2)) are not equivalent for C-p(X). These results answer questions posed by Shakhmatov. Concerning properties (alpha(i)) for C-p(X), some results on Scheepers' conjecture are also given.