Intersection of a sequence of outer models, part 1

The technique of taking the intersection of a sequence of outer models is understudied in the field of Mathematical Logic. With Assaf Rinot and Jiachen Yuan, we find it to be quite effective for constructing some interesting sum ultrafilters. In this talk, I will first illustrate how we use it to answer questions about indecomposable ultrafilters and $\delta$-complete uniform ultrafilters, and then extend some results in infinitary combinatorics. A sample result is that we construct a model in which there exists a weakly compact cardinal that carries an indecomposable ultrafilter but not measurable, thus answering an old question of Ketonen in the negative.