I think I have found the answer to my own question. Since I cannot post it here, I have posted it as an answer to the related question cited above. I hope it will be useful, since I have not been able to find it in any book I have had at hand.

Thank you very much. The answer is, thus, that, by adding $\aleph_2$ random reals to a model of GCH, a model is obtained in which $[0,1]$ is a union of $\aleph_1$ pairwise disjoint closed sets.

I guess that Ramanujan's "theorem" depends on the conjecture about powers of primes, exactly as Erdős' conjecture does, but, since it is stated as a theorem everywhere, I would like to know the opinion of an expert.

Thank you!, but you are not choosing $B$ in any particular way, and in general, $B$ is not necessarily meager. Consider the trivial case in which $A=\emptyset$. You can take $p\subset B_0=\{x\in {}^\omega2 : x(0)=0\}$ and $B=B_1\times{}^\omega 2$. Then $p \Vdash B_{\mathring{c}} = \mathring{A}$, but $B$ is not meager.