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| Rupert... |
 Posted: Sat Oct 31, 2009 6:34 pm |
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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. How do you do that? |
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