Platek Spaces

Abstract

The aim of this work is to axiomatize and enhance the recursion theory on monotonic hierarchies of operative spaces developed in [1]. This is to be accomplished by employing a special new variety of operative spaces called Platek spaces. The original structure studied by Platek in [2] corresponds to the particular Platek space with structural class O=ω and a bottom operative space consisting of single-valued partial functions over an arbitrary domain (Example 1.1 below). We believe that Platek spaces not only redefine Platek's approach in an abstract manner, but also provide the appropriate setting for an intrinsic Generalized Recursion Theory.