abstract
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Making doughnuts of Cohen reals

Lorenz Halbeisen

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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*.
A set *S* of infinite subsets of natural numbers has the *doughnut
property*, if it contains or is disjoint from a doughnut. It
is known that not every such set *S* has the doughnut property,
but *S* has the doughnut property if it has the Baire property
or the Ramsey property. In this paper it is shown that a
finite support iteration of length *omega*_{1} of Cohen
forcing, starting from *L*, yields a model for CH + "all Sigma-1-2
sets have the doughnut property" + "not all Sigma-1-2
sets are Ramsey" + "not all Sigma-1-2 sets have the Baire property".