most recent 30 from http://mathoverflow.net 2013-05-19T00:40:57Z http://mathoverflow.net/feeds/question/19039 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/19039/an-interesting-statement-about-definability-in-set-theory-is-it-true-false-or-u Garabed Gulbenkian 2010-03-22T17:18:14Z 2010-03-22T17:18:14Z

<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://mathoverflow.net/questions/17608/a-question-about-ordinal-definable-real-numbers" rel="nofollow">A question about ordinal definable real numbers</a> </p> </blockquote> <p>Does anybody know whether there is a theorem of ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice) stating that if S is any ordinal definable set of real numbers at least one of whose elements is a real number which is not ordinal definable, then S is necessarily uncountable? Or is the provability of this statement in ZFC-assuming ZFC is consistent-actually an open question?</p>