… Mitchell in [M74], where it arises naturally in connection with inner models and coherent
sequences. Mitchell … < is now known as the Mitchell order, although it is not actually an order. It is …

… rank of U with respect to the ordering <]. If K is a cardinal then O(K) = {o(U): U is an ultrafilter
… in M and because of the absoluteness of well-foundedness we would be done except that D …

… We define here the well ordering of parameters which is used in this paper. When the first …
h(ck+1) for all keo), contradicting the well foundedness of M. Thus the construction of (ck:ke w) …

… We now return to the models L and L[U] in order to look at another direction in which the …
To prove clause 3.19(3), note that by the absoluteness of well-foundedness we can find, …

… In Section 4 we prove that the Mitchell order is wellfounded on downward closed extenders
below rank-to-rank type. The restriction of downward closure (see Section 2 for the definition) …

… the study of the Mitchell order in the ill-founded case, and address question (ii). Specifically,
we focus on the extent to which the well-foundedness of the Mitchell order fails on rank-to-…

… Although we will be interested only in well-founded models, note that wellfoundedness of
Ult(… V = L[l/] (which is Mitchell's model having PK as the linear order of size q). U and K are also …

… The lengths ~ and/~t of the iterated ultrapowers then determine the order of the the mice. …
There is no need to worry about the well foundedness of ultrapowers of the core model by W, …

… L, Mitchell showed that the partial order ◃ is well-founded, and this fact allowed a definition
of the order … Mitchell used what he later termed a µ-measurable cardinal to obtain sequences …

… In all of our applications the model M will have a definable well-ordering which provides
Skolem functions that ensure this. Definition 1.4 can also be used in cases when M is a well-…