most recent 30 from http://mathoverflow.net 2013-05-18T22:27:50Z http://mathoverflow.net/feeds/question/109005 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109005/decidability-of-the-generated-order Lilach Leibovich 2012-10-06T15:18:07Z 2012-10-06T16:48:18Z

<p>is the question whether a polynomial is non-negative on some semi-algebraic set (equivalently, is it in the cone denerated by some polynomials in the field of rational functions) known to be decidable?</p>

http://mathoverflow.net/questions/109005/decidability-of-the-generated-order/109013#109013 Andreas Blass 2012-10-06T16:48:18Z 2012-10-06T16:48:18Z

<p>Assuming you're working over the real numbers (or at least over a real-closed field), the answer is yes. The question lies within the first-order theory of real-closed fields, and that theory is decidable by an old theorem of Tarski. </p>