Alex Kiselev claims to have shown “There are no weakly inaccessible cardinals” in Zermelo-Fraenkel set theory (ZF). This would have the consequence that strongly inaccessible cardinals don’t exist either and so on for all the other large cardinals. Martin Davis on the FOM list cautions that the claim is “highly dubious”.

Here are links to Kiselev’s papers:

Part 1: http://arxiv.org/abs/1010.1956

Part 2: http://arxiv.org/abs/1011.1447

Link to the FOM list entry: http://www.cs.nyu.edu/pipermail/fom/2011-August/015694.html

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