Logic and Set Theory: A hierarchy of Ramsey cardinals
Peter Holy, Hausdorff Centre, University of Bonn
I will introduce a hierarchy of large cardinal notions in the area of Ramsey cardinals, that in particular are closely related to Victoria Gitman's Ramsey-like cardinals. I will show this hierarchy to be a proper hierarchy, and the cardinals in this hierarchy to have a range of equivalent characterizations, using either infinite games, elementary embeddings or filters. I will try to argue that the cardinals kappa that top our hierarchy, which are what we call the kappa-Ramsey cardinals, may be seen as a more natural (and slightly stronger) version of Gitman's super Ramsey cardinals. This is joint work with Philipp Schlicht.