For a ⊆ b ⊆ ω with b\a infinite, the set D = {x ∈ [ω] : a ⊆ x ⊆ b} is called a doughnut. Doughnuts are equivalent to conditions of Silver forcing, and so, a set S ⊆ [ω] is called Silver measurable, also known as completely doughnut, if for every doughnut D there is a doughnut D′ ⊆ D which is contained or disjoint from S. In this paper, we investigate the Silver measurability of ∆2 and Σ 1 2 set...
