The prime number theorem is PRA-provable

https://doi.org/10.1016/S0304-3975(00)00116-XGet rights and content
Under an Elsevier user license
open archive

Abstract

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.

Résumé

On introduit plusieurs théories dont le langage est assez riche pour parler des objets usuels de l'analyse réelle et complexe, et dont les axiomes permettent de retrouver beaucoup de résultats classiques, avec parfois quelques modifications. On montre que ces théories sont des extensions conservatrices de l'Arithmétique Primitive Récursive (PRA). Enfin, à titre d'exemple de leur intérêt, on montre que le théorème des nombres premiers est PRA-prouvable.

Keywords

Primitive recursive arithmetic
Recursive analysis
Analytical number theory

Cited by (0)

1

I would like to thank Professor P. Cegielski who provided many corrections and improvements.