If R^# exists then why is cof(\theta^{L(R)}) = \omega? Also I have the same question for the L(V_{\lambda+1}) generalization (if it's actually a different proof; I presume it isn't), i.e. if \theta is defined as the sup of the surjections in L(V_{\lambda+1}) of V_{\lambda+1} onto an ordinal, then if V_{\lambda+1}^# exists why is cof(\theta^{L(V_{\lambda+1})}) = \omega?