most recent 30 from http://mathoverflow.net 2013-05-19T05:44:40Z http://mathoverflow.net/feeds/user/27034 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108955/unboundedness-of-primes-in-bounded-arithmetic shahram 2012-10-05T20:11:08Z 2012-10-06T08:59:24Z

<p>Wilkie's well known question asks whether $I\Delta_{0}$ proves the unboundedness of primes. We know that by adding a sentence to $I\Delta_{0}$ which says "the exponential function is total", it is possible to prove the unboundedness of primes. This sentence is $\Pi_{2}$. Suppose $\Pi_{1}-Th(\mathbb{N})$ denotes the set of all $\Pi_{1}$ sentences that are true in $\mathbb{N}$. My question is:</p> <p>Is it known that $I\Delta_{0} +\Pi_{1}-Th(\mathbb{N})$ proves the unboundedness of primes?</p>

http://mathoverflow.net/questions/108955/unboundedness-of-primes-in-bounded-arithmetic/108988#108988 shahram 2012-10-06T10:34:50Z 2012-10-06T10:34:50Z

Thanks for your interesting answer and the link!