  A set of reals is perfect iff it is nonempty, closed and contains no isolated points. The key feature of this for our purposes is that if a set of reals contains a perfect subset then it must have the same size as the continuum (i.e., the reals). A set of reals is said to have the perfect set property iff it is either countable or contains a perfect subset. The interest of this property is that the sets of reals with the perfect set property satisfy CH. In early work, Cantor and Bendixson established (in 1883) that all closed sets have the perfect set property. Thus, there is no closed counter-example to the continuum hypothesis. Later, in 1903, Young showed that the Π̰02 sets have the perfect set property. A central question was how far this property propagates. Do all of the Borel sets of reals have the perfect set property? Do all of the projective sets of reals have the perfect set property? 