An inner model theoretic proof of Becker's theorem

Abstract

We give a new proof of a theorem of Becker that under AD+V=L(R), omega_2 is a kappa-supercompact for every kappa less than or equal to the supremum of all Suslin cardinals. Our proof uses inner model theory. It is still open whether one can prove, say under AD_R, that Suslin cardinals and their successors are <Theta-supercompact. That this is true is a theorem of Steve Jackson, who proved it using generic codes.