  In this article we compare the well-known Ramsey property with a dual form of
it, the so called dual-Ramsey property (which was suggested first by Carlson
and Simpson). Even if the two properties are different, it can be shown that
all classical results known for the Ramsey property also hold for the
dual-Ramsey property. We will also show that the dual-Ramsey property is closed
under a generalized Suslin operation (the similar result for the Ramsey
property was proved by Matet). Further we compare two notions of forcing, the
Mathias forcing and a dual form of it, and will give some symmetries between
them. Finally we give some relationships between the dual-Mathias forcing and
the dual-Ramsey property.
