abstract
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Silver measurability and its relation to other regularity properties

Jörg Brendle, Lorenz Halbeisen, and Benedikt Löwe

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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.