Kurepa-trees and Namba-forcing
  We show that compact cardinals and {\rm MM} are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding 'regressive' $\lambda$-Kurepa-trees in either case. We argue that the destruction of regressive Kurepa-trees with {\rm MM} requires the use of Namba forcing. 
Bernhard Koenig (ELM), Yasuo Yoshinobu (NAGOYA)