Autonomous Fixed Point Progressions and Fixed Point Transfinite Recursion
Thomas Strahm · Cambridge University Press eBooks · 2017
. This paper is a contribution to the area of metapredicative proof theory. It continues recent investigations on the transfinitely iterated fixed point theories # ID# (cf. [10]) and addresses the question of autonomity in iterated fixed point theories. An external and an internal form of autonomous generation of transfinite hierarchies of fixed points of positive arithmetic operators are introduced and proof-theoretically analyzed. This includes the discussion of the principle of so-called fixed point transfinite recursion. Connections to theories for iterated inaccessibility in the context of Kripke Platek set theory without foundation are revealed. 1 Introduction The foundational program to study the principles and ordinals which are implicit in a predicative conception of the universe of sets of natural numbers led to the progression of systems of ramified analysis up to the famous Feferman-Schutte ordinal # 0 in the early sixties. Since then numerous theories have been found w...