The algebraic sum of a set of strong measure zero and a perfectly meager set revisited (Q2717957)

In this paper the authors give a simpler proof of a theorem proved by the first author [East-West J. Math. 1, 171-178 (1999; Zbl 0944.03045)]: it is consistent with ZFC that there exist subsets \(X\) and \(Y\) of the Cantor space \(2^\omega\) such that \(X\) is strongly measure zero, \(Y\) is perfectly meager, and the algebraic sum \(X+Y\) contains a perfect set. They also show that it is consistent with ZFC that there exist \(X\) and \(Y\) such that \(X\) is universal measure zero, \(Y\) is strongly meager, and \(X+Y\) contains a perfect set.