The linearity of the Mitchell order
The linearity of the Mitchell order
We show from an abstract comparison principle (the Ultrapower Axiom) that the Mitchell order is linear on sufficiently strong ultrafilters: normal ultrafilters, Dodd solid ultrafilters, and assuming GCH, generalized normal ultrafilters. This gives a conditional answer to the well-known question of whether a [Formula: see text]-supercompact cardinal [Formula: see text] …