Optimal proofs of determinacy

 

Itay Neeman

 

 

Abstract:

 

This paper announces a method for proving determinacy from large

cardinals which, in many cases, yields optimal results. Two

applications are presented. The first extends theorems of Martin

and Steel on determinacy within the projective hierarchy, and

the second gives a new proof of Woodin’s theorem on determinacy

in $L({\mathbb R})$.