Fixed points in Peano arithmetic with ordinals

Abstract

Jäger, G., Fixed points in Peano arithmetic with ordinals, Annals of Pure and Applied Logic 60 (1993) 119-132. This paper deals with some proof-theoretic aspects of fixed point theories over Peano arithmetic with ordinals. It studies three such theories which differ in the principles which are available for induction on the natural numbers and ordinals. The main result states that there is a natural theory in this framework which is a conservative extension of Peano arithmetic. © 1993.