The prime number theorem is PRA-provable
We introduce several theories the language of which is rich enough to talk about usual objects of real and complex analysis, and the axioms of which allow to recover a lot of classical results (sometimes with slight modifications). We prove that these theories are conservative extensions of primitive recursive arithmetic (PRA) and develop analysis within them. Moreover, as an example of their efficiency, we shall prove that the prime number theorem is PRA-provable. (C) 2001 Elsevier Science B.V. All rights reserved.
primitive recursive arithmetic recursive analysis analytical number theory