We present some new results on union ultrafilters. We characterize stability for union ultrafilters and, as the main result, we construct a new kind of unordered union ultrafilter.

No abstract

No abstract

We present some new results on strongly summable ultrafilters. As the main result, we extend a theorem by N. Hindman and D. Strauss on writing strongly summable ultrafilters as sums.

This short note contains the proofs of two small but somewhat surprising results about ultrafilters on N: 1. strongly summable ultrafilters are rapid, 2. every rapid ultrafilter induces a closed left ideal of rapid ultrafilters. As a consequence, there will be rapid minimal idempotents in all models of set theory with rapid ultrafilters.The history of this result has been published as an experiment in mathematical writing on the author's website [Kra121], [Kra122] where you can can also find additional remarks by Andreas R. Blass and Neil Hindman, offering a form of peer-review.