Symmetries between two Ramsey properties [article]

Lorenz Halbeisen
2001 arXiv   pre-print
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
more » ... are 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.
arXiv:math/0109101v1 fatcat:k2bk3a5iynbnhevegwsum7papa