Abstract

In [3], Shi proved that there exist incomparable Zermelo degrees at γ if there exists an ω‐sequence of measurable cardinals, whose limit is γ. He asked whether there is a size antichain of Zermelo degrees. We consider this question for the ‐degree structure. We use a kind of Prikry‐type forcing to show that if there is an ω‐sequence of measurable cardinals, then there are ‐many pairwise incomparable ‐degrees, where γ is the limit of the ω‐sequence of measurable cardinals.