Silver measurability and its relation to other regularity properties

For a subset of b subset of w with b\a infinite, the set D = {x is an element of [omega](omega) : a subset of x subset of b} is called a doughnut. Doughnuts are equivalent to conditions of Silver forcing, and so, a set S subset of [omega](omega) is is called Silver measurable, or completely doughnut, if for every doughnut D there is a doughnut D' subset of D which is contained in or disjoint from S. In this paper, we investigate the Silver measurability of Delta(1)(2) and Sigma(1)(2) sets of reals and compare it to other regularity properties like the Baire and the Ramsey property and Miller and Sacks measurability.