**September 18**

Arthur Apter,
CUNY

**UA and the Number of Normal Measures over $\aleph_{\omega + 1}$**

The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.