Autonomous fixed point progressions and fixed point transfinite recursion
نویسنده
چکیده
This paper is a contribution to the area of metapredicative proof theory. It continues recent investigations on the transfinitely iterated fixed point theories ÎDα (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.
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