On perfectly meager sets
  A set of reals A is called perfectly meager if A \cap P is meager in P, for every perfect set P. Marczewski asked if the product of perfectly meager sets is perfectly meager. In the paper it is shown that it is consistent that the answer to this question is positive. (It is known that it is also consistent that the answer is negative (Reclaw)) 
Tomek Bartoszynski