Silver measurability and its relation to other regularity properties

For subsets of natural numbers a and b where b-a is infinite, the set of all infinite sets which are contained in b and containing a is called a doughnut. Doughnuts are equivalent to conditions of Silver forcing, and so, a subset of the real line S is called Silver measurable, or completely doughnut, if every doughnut D contains a doughnut 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.

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