On disjoint stationary sequences

Abstract

We answer a question of Krueger by obtaining disjoint stationary sequences on successive cardinals. The main idea is an alternative presentation of a mixed support iteration, using it even more explicitly as a variant of Mitchell forcing. We also use a Mahlo cardinal to obtain a model in which ${\aleph }_2\notin I[{\aleph }_2]$ and there is no disjoint stationary sequence on ${\aleph }_2$, answering a question of Gilton.

Substantial changes to the proof of Theorem 3, which is now only stated for ${\aleph }_2$. Amendments to the proof of Theorem 2. Other small changes throughout