# Topic Archive: Mitchell order

Set theory seminarFriday, October 9, 201510:00 amGC 3212

# The Mitchell order for Ramsey cardinals

The usual Mitchell relation on normal measures on a measurable cardinal $\kappa$ orders the measures based on the degree of measurability that $\kappa$ retains in their respective ultrapowers. We shall examine the analogous ordering of appropriate witnessing objects for Ramsey (and Ramsey-like) cardinals. It turns out that the resulting order is well-behaved and its degrees neatly stratify the large cardinal hierarchy between Ramsey, strongly Ramsey, and super Ramsey cardinals. We also give a soft killing argument for this notion of Mitchell rank.