most recent 30 from http://mathoverflow.net 2013-05-23T02:54:28Z http://mathoverflow.net/feeds/user/26261 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106522/why-cant-an-explicit-well-ordering-of-the-reals-be-ruled-out-in-zf/106524#106524 Cody Dance 2012-09-06T15:54:03Z 2012-09-06T15:54:03Z

<p>Here is the error in your reasoning "If B were true, then A would be provable in ZF, which is impossible since A is independent of ZF, so B must be false." The statement "B is independent of ZF" means that there are models of ZF where it is true (V=L) and models where it is false(almost everything else). You are right in saying that in a model where B is true, then A is true but that does not mean that A is provable from ZF. There are also models where A is true and B is false (i.e. if we assume choice that will give us a well ordering, but that does not mean that it is definable.)</p>