# The Mitchell order for Ramsey cardinals

## Miha Habič

### The CUNY Graduate Center

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.

This is joint work with Victoria Gitman and Erin Carmody.

Miha Habič is a graduate student at the CUNY GC. He got his Masters Degree in Mathematics at the University of Ljubljana, Slovenia. His interests lie in the area of infinitary computability, forcing and large cardinals.