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Platek spaces

Ivanov L.

Fundamenta Informaticae

2000

Vol. 44, Nr 1,2

145-181

The aim of this work is to axiomatize and enhance the recursion theory on monotonic hierarchies of operative spaces developed. This is to be accomplished by employing a special new variety of operative spaces called Platek spaces. The original structure studied by Platek in corresponds to the particular Platek space with structural class O = w 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.

Boldface recursion on Platek spaces

Ivanov L.

Fundamenta Informaticae

2000

Vol. 44, Nr 1,2

183-208

The present work develops a boldface version of the theory of Platek spaces initiated. This is done by studying recursion on spaces with special elements which embody the so called transfer operation, Chapter 14 affording full lambda-abstraction. Transfer is characteristic of the monotonic hierarchies of operative spaces, which hierarchies form models of a typed lambda-mu-calculus. The principal result here is a boldface version of the abstract Platek First Recursion Theorem; we prove appropriate boldface Enumeration and Second Recursion Theorems as well.