On disjoint stationary sequences

We answer a question of Krueger by obtaining disjoint stationary sequences<br>on successive cardinals. The main idea is an alternative presentation of a<br>mixed support iteration, using it more explicitly as a variant of Mitchell<br>forcing. We also use a Mahlo cardinal to obtain a model in which ℵ2 ∈/ I[ℵ2]<br>and there is no disjoint stationary sequence on ℵ2, answering a question<br>of Gilton.