Making doughnuts of Cohen reals
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 omega1 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".