Assuming the existence of a measurable cardinal, we define a hierarchy of Ramsey cardinals and a hierarchy of normal filters. We study some combinatorial properties of this hierarchy. We show that this hierarchy is absolute with respect to the Dodd-Jensen core model, extending a result of Mitchell which says that being Ramsey is absolute with respect to the core model.

Reviewed Works:John R. Steel, A. S. Kechris, D. A. Martin, Y. N. Moschovakis, Scales on $\Sigma^1_1$ Sets.Yiannis N. Moschovakis, Scales on Coinductive Sets.Donald A. Martin, John R. Steel, The Extent of Scales in $L$.John R. Steel, Scales in $L$.