KUREPA TREES AND NAMBA FORCING

We show that strongly compact cardinals and MM are sensitive to lambda-closed foreings 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 requires a non-standard application of MM. As a corollary, we find a consistent example of an omega(2)-closed poset that is not forcing equivalent to any omega(2)-directed-closed poset.