[FOM] paradoxical partitions of the unit ball

[Rupert McCallum]

Let IC be the assertion that there is an inaccessible cardinal. 
Solovay proved that if ZFC+IC is consistent, then so is ZFC+"Every 
projective set of reals is Lebesgue measurable". If every projective 
set of reals is Lebesgue measurable, then there is no paradoxical 
partition of the unit ball using projective pieces. But in 

 
http://www.ams.org/notices/200106/fea-woodin.pdf 
 
Woodin states that the consistency of ZFC+"There is no paradoxical 
partition of the unit ball using projective pieces" can be proved just 
on the assumption that ZFC is consistent. Where can I find the proof of this result?


Dr Rupert McCallum
Lecturer in Mathematics
(02) 9701 4050