Woodin, W. Hugh. 2015. The weak ultrafilter axiom. Archive for Mathematical Logic 55 (1): 319–351. doi:10.1007/s00153-015-0467-2.
The main theorem is that the Ultrafilter Axiom of Woodin (J Math Log 11(2):115–37, 2011) must fail at all cardinals where the Axiom I0 holds, in all non-strategic extender models subject only to fairly general requirements on the non-strategic extender model.