Applications of the Magidor Iteration to Ultrafilter Theory
Logic
2026-04-22 v2
Abstract
We characterize sums of normal ultrafilters after the Magidor iteration (product) of Prikry forcings over a discrete set of measurable cardinals. We apply this to show that the weak Ultrapower Axiom is not equivalent to the Ultrapower Axiom. We also construct a non-rigid ultrapower and two uniform ultrafilters on different cardinals that have the same ultrapower.
Cite
@article{arxiv.2412.09683,
title = {Applications of the Magidor Iteration to Ultrafilter Theory},
author = {Tom Benhamou and Gabriel Goldberg},
journal= {arXiv preprint arXiv:2412.09683},
year = {2026}
}