User shahram - MathOverflow 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 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 Comment by shahram shahram 2012-10-06T10:34:50Z 2012-10-06T10:34:50Z Thanks for your interesting answer and the link!