Ed Nelson has now withdrawn his claim. http://www.cs.nyu.edu/pipermail/fom/2011-October/015832.html http://www.cs.nyu.edu/pipermail/fom/2011-October/015832.htm

Ed Nelson has now withdrawn his claim. http://www.cs.nyu.edu/pipermail/fom/2011-October/015832.html http://www.cs.nyu.edu/pipermail/fom/2011-October/015832.html Terrence Tao, at http://golem.ph.utexas.edu/category/2011/09/ and independently Daniel Tausk (private communication) have found an irreparable error in my outline. In the Kritchman-Raz proof, there is a low complexity proof of K(\bar\xi)>\ell if we assume \mu=1, but the Chaitin machine may find a shorter proof of high complexity, with no control over how high. My thanks to Tao and Tausk for spotting this. I withdraw my claim. The consistency of P remains an open problem.